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Understanding Data Presentations (Guide + Examples)

In this age of overwhelming information, the skill to effectively convey data has become extremely valuable. Initiating a discussion on data presentation types involves thoughtful consideration of the nature of your data and the message you aim to convey. Different types of visualizations serve distinct purposes. Whether you’re dealing with how to develop a report or simply trying to communicate complex information, how you present data influences how well your audience understands and engages with it. This extensive guide leads you through the different ways of data presentation.

Table of Contents

What is a Data Presentation?

What should a data presentation include, line graphs, treemap chart, scatter plot, how to choose a data presentation type, recommended data presentation templates, common mistakes done in data presentation.

A data presentation is a slide deck that aims to disclose quantitative information to an audience through the use of visual formats and narrative techniques derived from data analysis, making complex data understandable and actionable. This process requires a series of tools, such as charts, graphs, tables, infographics, dashboards, and so on, supported by concise textual explanations to improve understanding and boost retention rate.

Data presentations require us to cull data in a format that allows the presenter to highlight trends, patterns, and insights so that the audience can act upon the shared information. In a few words, the goal of data presentations is to enable viewers to grasp complicated concepts or trends quickly, facilitating informed decision-making or deeper analysis.

Data presentations go beyond the mere usage of graphical elements. Seasoned presenters encompass visuals with the art of data storytelling , so the speech skillfully connects the points through a narrative that resonates with the audience. Depending on the purpose – inspire, persuade, inform, support decision-making processes, etc. – is the data presentation format that is better suited to help us in this journey.

To nail your upcoming data presentation, ensure to count with the following elements:

• Clear Objectives: Understand the intent of your presentation before selecting the graphical layout and metaphors to make content easier to grasp.
• Engaging introduction: Use a powerful hook from the get-go. For instance, you can ask a big question or present a problem that your data will answer. Take a look at our guide on how to start a presentation for tips & insights.
• Structured Narrative: Your data presentation must tell a coherent story. This means a beginning where you present the context, a middle section in which you present the data, and an ending that uses a call-to-action. Check our guide on presentation structure for further information.
• Visual Elements: These are the charts, graphs, and other elements of visual communication we ought to use to present data. This article will cover one by one the different types of data representation methods we can use, and provide further guidance on choosing between them.
• Insights and Analysis: This is not just showcasing a graph and letting people get an idea about it. A proper data presentation includes the interpretation of that data, the reason why it’s included, and why it matters to your research.
• Conclusion & CTA: Ending your presentation with a call to action is necessary. Whether you intend to wow your audience into acquiring your services, inspire them to change the world, or whatever the purpose of your presentation, there must be a stage in which you convey all that you shared and show the path to staying in touch. Plan ahead whether you want to use a thank-you slide, a video presentation, or which method is apt and tailored to the kind of presentation you deliver.
• Q&A Session: After your speech is concluded, allocate 3-5 minutes for the audience to raise any questions about the information you disclosed. This is an extra chance to establish your authority on the topic. Check our guide on questions and answer sessions in presentations here.

Bar charts are a graphical representation of data using rectangular bars to show quantities or frequencies in an established category. They make it easy for readers to spot patterns or trends. Bar charts can be horizontal or vertical, although the vertical format is commonly known as a column chart. They display categorical, discrete, or continuous variables grouped in class intervals [1] . They include an axis and a set of labeled bars horizontally or vertically. These bars represent the frequencies of variable values or the values themselves. Numbers on the y-axis of a vertical bar chart or the x-axis of a horizontal bar chart are called the scale.

Real-Life Application of Bar Charts

Let’s say a sales manager is presenting sales to their audience. Using a bar chart, he follows these steps.

Step 1: Selecting Data

The first step is to identify the specific data you will present to your audience.

The sales manager has highlighted these products for the presentation.

• Product A: Men’s Shoes
• Product B: Women’s Apparel
• Product C: Electronics
• Product D: Home Decor

Step 2: Choosing Orientation

Opt for a vertical layout for simplicity. Vertical bar charts help compare different categories in case there are not too many categories [1] . They can also help show different trends. A vertical bar chart is used where each bar represents one of the four chosen products. After plotting the data, it is seen that the height of each bar directly represents the sales performance of the respective product.

It is visible that the tallest bar (Electronics – Product C) is showing the highest sales. However, the shorter bars (Women’s Apparel – Product B and Home Decor – Product D) need attention. It indicates areas that require further analysis or strategies for improvement.

Step 3: Colorful Insights

Different colors are used to differentiate each product. It is essential to show a color-coded chart where the audience can distinguish between products.

• Men’s Shoes (Product A): Yellow
• Women’s Apparel (Product B): Orange
• Electronics (Product C): Violet
• Home Decor (Product D): Blue

Bar charts are straightforward and easily understandable for presenting data. They are versatile when comparing products or any categorical data [2] . Bar charts adapt seamlessly to retail scenarios. Despite that, bar charts have a few shortcomings. They cannot illustrate data trends over time. Besides, overloading the chart with numerous products can lead to visual clutter, diminishing its effectiveness.

For more information, check our collection of bar chart templates for PowerPoint .

Line graphs help illustrate data trends, progressions, or fluctuations by connecting a series of data points called ‘markers’ with straight line segments. This provides a straightforward representation of how values change [5] . Their versatility makes them invaluable for scenarios requiring a visual understanding of continuous data. In addition, line graphs are also useful for comparing multiple datasets over the same timeline. Using multiple line graphs allows us to compare more than one data set. They simplify complex information so the audience can quickly grasp the ups and downs of values. From tracking stock prices to analyzing experimental results, you can use line graphs to show how data changes over a continuous timeline. They show trends with simplicity and clarity.

Real-life Application of Line Graphs

To understand line graphs thoroughly, we will use a real case. Imagine you’re a financial analyst presenting a tech company’s monthly sales for a licensed product over the past year. Investors want insights into sales behavior by month, how market trends may have influenced sales performance and reception to the new pricing strategy. To present data via a line graph, you will complete these steps.

First, you need to gather the data. In this case, your data will be the sales numbers. For example:

• January: $45,000
• February: $55,000
• March: $45,000
• April: $60,000
• May: $ 70,000
• June: $65,000
• July: $62,000
• August: $68,000
• September: $81,000
• October: $76,000
• November: $87,000
• December: $91,000

After choosing the data, the next step is to select the orientation. Like bar charts, you can use vertical or horizontal line graphs. However, we want to keep this simple, so we will keep the timeline (x-axis) horizontal while the sales numbers (y-axis) vertical.

Step 3: Connecting Trends

After adding the data to your preferred software, you will plot a line graph. In the graph, each month’s sales are represented by data points connected by a line.

Step 4: Adding Clarity with Color

If there are multiple lines, you can also add colors to highlight each one, making it easier to follow.

Line graphs excel at visually presenting trends over time. These presentation aids identify patterns, like upward or downward trends. However, too many data points can clutter the graph, making it harder to interpret. Line graphs work best with continuous data but are not suitable for categories.

For more information, check our collection of line chart templates for PowerPoint and our article about how to make a presentation graph .

A data dashboard is a visual tool for analyzing information. Different graphs, charts, and tables are consolidated in a layout to showcase the information required to achieve one or more objectives. Dashboards help quickly see Key Performance Indicators (KPIs). You don’t make new visuals in the dashboard; instead, you use it to display visuals you’ve already made in worksheets [3] .

Keeping the number of visuals on a dashboard to three or four is recommended. Adding too many can make it hard to see the main points [4]. Dashboards can be used for business analytics to analyze sales, revenue, and marketing metrics at a time. They are also used in the manufacturing industry, as they allow users to grasp the entire production scenario at the moment while tracking the core KPIs for each line.

Real-Life Application of a Dashboard

Consider a project manager presenting a software development project’s progress to a tech company’s leadership team. He follows the following steps.

Step 1: Defining Key Metrics

To effectively communicate the project’s status, identify key metrics such as completion status, budget, and bug resolution rates. Then, choose measurable metrics aligned with project objectives.

Step 2: Choosing Visualization Widgets

After finalizing the data, presentation aids that align with each metric are selected. For this project, the project manager chooses a progress bar for the completion status and uses bar charts for budget allocation. Likewise, he implements line charts for bug resolution rates.

Step 3: Dashboard Layout

Key metrics are prominently placed in the dashboard for easy visibility, and the manager ensures that it appears clean and organized.

Dashboards provide a comprehensive view of key project metrics. Users can interact with data, customize views, and drill down for detailed analysis. However, creating an effective dashboard requires careful planning to avoid clutter. Besides, dashboards rely on the availability and accuracy of underlying data sources.

For more information, check our article on how to design a dashboard presentation , and discover our collection of dashboard PowerPoint templates .

Treemap charts represent hierarchical data structured in a series of nested rectangles [6] . As each branch of the ‘tree’ is given a rectangle, smaller tiles can be seen representing sub-branches, meaning elements on a lower hierarchical level than the parent rectangle. Each one of those rectangular nodes is built by representing an area proportional to the specified data dimension.

Treemaps are useful for visualizing large datasets in compact space. It is easy to identify patterns, such as which categories are dominant. Common applications of the treemap chart are seen in the IT industry, such as resource allocation, disk space management, website analytics, etc. Also, they can be used in multiple industries like healthcare data analysis, market share across different product categories, or even in finance to visualize portfolios.

Real-Life Application of a Treemap Chart

Let’s consider a financial scenario where a financial team wants to represent the budget allocation of a company. There is a hierarchy in the process, so it is helpful to use a treemap chart. In the chart, the top-level rectangle could represent the total budget, and it would be subdivided into smaller rectangles, each denoting a specific department. Further subdivisions within these smaller rectangles might represent individual projects or cost categories.

Step 1: Define Your Data Hierarchy

While presenting data on the budget allocation, start by outlining the hierarchical structure. The sequence will be like the overall budget at the top, followed by departments, projects within each department, and finally, individual cost categories for each project.

• Top-level rectangle: Total Budget
• Second-level rectangles: Departments (Engineering, Marketing, Sales)
• Third-level rectangles: Projects within each department
• Fourth-level rectangles: Cost categories for each project (Personnel, Marketing Expenses, Equipment)

Step 2: Choose a Suitable Tool

It’s time to select a data visualization tool supporting Treemaps. Popular choices include Tableau, Microsoft Power BI, PowerPoint, or even coding with libraries like D3.js. It is vital to ensure that the chosen tool provides customization options for colors, labels, and hierarchical structures.

Here, the team uses PowerPoint for this guide because of its user-friendly interface and robust Treemap capabilities.

Step 3: Make a Treemap Chart with PowerPoint

After opening the PowerPoint presentation, they chose “SmartArt” to form the chart. The SmartArt Graphic window has a “Hierarchy” category on the left.  Here, you will see multiple options. You can choose any layout that resembles a Treemap. The “Table Hierarchy” or “Organization Chart” options can be adapted. The team selects the Table Hierarchy as it looks close to a Treemap.

Step 5: Input Your Data

After that, a new window will open with a basic structure. They add the data one by one by clicking on the text boxes. They start with the top-level rectangle, representing the total budget.  

Step 6: Customize the Treemap

By clicking on each shape, they customize its color, size, and label. At the same time, they can adjust the font size, style, and color of labels by using the options in the “Format” tab in PowerPoint. Using different colors for each level enhances the visual difference.

Treemaps excel at illustrating hierarchical structures. These charts make it easy to understand relationships and dependencies. They efficiently use space, compactly displaying a large amount of data, reducing the need for excessive scrolling or navigation. Additionally, using colors enhances the understanding of data by representing different variables or categories.

In some cases, treemaps might become complex, especially with deep hierarchies.  It becomes challenging for some users to interpret the chart. At the same time, displaying detailed information within each rectangle might be constrained by space. It potentially limits the amount of data that can be shown clearly. Without proper labeling and color coding, there’s a risk of misinterpretation.

A heatmap is a data visualization tool that uses color coding to represent values across a two-dimensional surface. In these, colors replace numbers to indicate the magnitude of each cell. This color-shaded matrix display is valuable for summarizing and understanding data sets with a glance [7] . The intensity of the color corresponds to the value it represents, making it easy to identify patterns, trends, and variations in the data.

As a tool, heatmaps help businesses analyze website interactions, revealing user behavior patterns and preferences to enhance overall user experience. In addition, companies use heatmaps to assess content engagement, identifying popular sections and areas of improvement for more effective communication. They excel at highlighting patterns and trends in large datasets, making it easy to identify areas of interest.

We can implement heatmaps to express multiple data types, such as numerical values, percentages, or even categorical data. Heatmaps help us easily spot areas with lots of activity, making them helpful in figuring out clusters [8] . When making these maps, it is important to pick colors carefully. The colors need to show the differences between groups or levels of something. And it is good to use colors that people with colorblindness can easily see.

Check our detailed guide on how to create a heatmap here. Also discover our collection of heatmap PowerPoint templates .

Pie charts are circular statistical graphics divided into slices to illustrate numerical proportions. Each slice represents a proportionate part of the whole, making it easy to visualize the contribution of each component to the total.

The size of the pie charts is influenced by the value of data points within each pie. The total of all data points in a pie determines its size. The pie with the highest data points appears as the largest, whereas the others are proportionally smaller. However, you can present all pies of the same size if proportional representation is not required [9] . Sometimes, pie charts are difficult to read, or additional information is required. A variation of this tool can be used instead, known as the donut chart , which has the same structure but a blank center, creating a ring shape. Presenters can add extra information, and the ring shape helps to declutter the graph.

Pie charts are used in business to show percentage distribution, compare relative sizes of categories, or present straightforward data sets where visualizing ratios is essential.

Real-Life Application of Pie Charts

Consider a scenario where you want to represent the distribution of the data. Each slice of the pie chart would represent a different category, and the size of each slice would indicate the percentage of the total portion allocated to that category.

Step 1: Define Your Data Structure

Imagine you are presenting the distribution of a project budget among different expense categories.

• Column A: Expense Categories (Personnel, Equipment, Marketing, Miscellaneous)
• Column B: Budget Amounts ($40,000, $30,000, $20,000, $10,000) Column B represents the values of your categories in Column A.

Step 2: Insert a Pie Chart

Using any of the accessible tools, you can create a pie chart. The most convenient tools for forming a pie chart in a presentation are presentation tools such as PowerPoint or Google Slides.  You will notice that the pie chart assigns each expense category a percentage of the total budget by dividing it by the total budget.

For instance:

• Personnel: $40,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 40%
• Equipment: $30,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 30%
• Marketing: $20,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 20%
• Miscellaneous: $10,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 10%

You can make a chart out of this or just pull out the pie chart from the data.

3D pie charts and 3D donut charts are quite popular among the audience. They stand out as visual elements in any presentation slide, so let’s take a look at how our pie chart example would look in 3D pie chart format.

Step 03: Results Interpretation

The pie chart visually illustrates the distribution of the project budget among different expense categories. Personnel constitutes the largest portion at 40%, followed by equipment at 30%, marketing at 20%, and miscellaneous at 10%. This breakdown provides a clear overview of where the project funds are allocated, which helps in informed decision-making and resource management. It is evident that personnel are a significant investment, emphasizing their importance in the overall project budget.

Pie charts provide a straightforward way to represent proportions and percentages. They are easy to understand, even for individuals with limited data analysis experience. These charts work well for small datasets with a limited number of categories.

However, a pie chart can become cluttered and less effective in situations with many categories. Accurate interpretation may be challenging, especially when dealing with slight differences in slice sizes. In addition, these charts are static and do not effectively convey trends over time.

For more information, check our collection of pie chart templates for PowerPoint .

Histograms present the distribution of numerical variables. Unlike a bar chart that records each unique response separately, histograms organize numeric responses into bins and show the frequency of reactions within each bin [10] . The x-axis of a histogram shows the range of values for a numeric variable. At the same time, the y-axis indicates the relative frequencies (percentage of the total counts) for that range of values.

Whenever you want to understand the distribution of your data, check which values are more common, or identify outliers, histograms are your go-to. Think of them as a spotlight on the story your data is telling. A histogram can provide a quick and insightful overview if you’re curious about exam scores, sales figures, or any numerical data distribution.

Real-Life Application of a Histogram

In the histogram data analysis presentation example, imagine an instructor analyzing a class’s grades to identify the most common score range. A histogram could effectively display the distribution. It will show whether most students scored in the average range or if there are significant outliers.

Step 1: Gather Data

He begins by gathering the data. The scores of each student in class are gathered to analyze exam scores.

After arranging the scores in ascending order, bin ranges are set.

Step 2: Define Bins

Bins are like categories that group similar values. Think of them as buckets that organize your data. The presenter decides how wide each bin should be based on the range of the values. For instance, the instructor sets the bin ranges based on score intervals: 60-69, 70-79, 80-89, and 90-100.

Step 3: Count Frequency

Now, he counts how many data points fall into each bin. This step is crucial because it tells you how often specific ranges of values occur. The result is the frequency distribution, showing the occurrences of each group.

Here, the instructor counts the number of students in each category.

• 60-69: 1 student (Kate)
• 70-79: 4 students (David, Emma, Grace, Jack)
• 80-89: 7 students (Alice, Bob, Frank, Isabel, Liam, Mia, Noah)
• 90-100: 3 students (Clara, Henry, Olivia)

Step 4: Create the Histogram

It’s time to turn the data into a visual representation. Draw a bar for each bin on a graph. The width of the bar should correspond to the range of the bin, and the height should correspond to the frequency.  To make your histogram understandable, label the X and Y axes.

In this case, the X-axis should represent the bins (e.g., test score ranges), and the Y-axis represents the frequency.

The histogram of the class grades reveals insightful patterns in the distribution. Most students, with seven students, fall within the 80-89 score range. The histogram provides a clear visualization of the class’s performance. It showcases a concentration of grades in the upper-middle range with few outliers at both ends. This analysis helps in understanding the overall academic standing of the class. It also identifies the areas for potential improvement or recognition.

Thus, histograms provide a clear visual representation of data distribution. They are easy to interpret, even for those without a statistical background. They apply to various types of data, including continuous and discrete variables. One weak point is that histograms do not capture detailed patterns in students’ data, with seven compared to other visualization methods.

A scatter plot is a graphical representation of the relationship between two variables. It consists of individual data points on a two-dimensional plane. This plane plots one variable on the x-axis and the other on the y-axis. Each point represents a unique observation. It visualizes patterns, trends, or correlations between the two variables.

Scatter plots are also effective in revealing the strength and direction of relationships. They identify outliers and assess the overall distribution of data points. The points’ dispersion and clustering reflect the relationship’s nature, whether it is positive, negative, or lacks a discernible pattern. In business, scatter plots assess relationships between variables such as marketing cost and sales revenue. They help present data correlations and decision-making.

Real-Life Application of Scatter Plot

A group of scientists is conducting a study on the relationship between daily hours of screen time and sleep quality. After reviewing the data, they managed to create this table to help them build a scatter plot graph:

In the provided example, the x-axis represents Daily Hours of Screen Time, and the y-axis represents the Sleep Quality Rating.

The scientists observe a negative correlation between the amount of screen time and the quality of sleep. This is consistent with their hypothesis that blue light, especially before bedtime, has a significant impact on sleep quality and metabolic processes.

There are a few things to remember when using a scatter plot. Even when a scatter diagram indicates a relationship, it doesn’t mean one variable affects the other. A third factor can influence both variables. The more the plot resembles a straight line, the stronger the relationship is perceived [11] . If it suggests no ties, the observed pattern might be due to random fluctuations in data. When the scatter diagram depicts no correlation, whether the data might be stratified is worth considering.

Choosing the appropriate data presentation type is crucial when making a presentation . Understanding the nature of your data and the message you intend to convey will guide this selection process. For instance, when showcasing quantitative relationships, scatter plots become instrumental in revealing correlations between variables. If the focus is on emphasizing parts of a whole, pie charts offer a concise display of proportions. Histograms, on the other hand, prove valuable for illustrating distributions and frequency patterns. 

Bar charts provide a clear visual comparison of different categories. Likewise, line charts excel in showcasing trends over time, while tables are ideal for detailed data examination. Starting a presentation on data presentation types involves evaluating the specific information you want to communicate and selecting the format that aligns with your message. This ensures clarity and resonance with your audience from the beginning of your presentation.

1. Fact Sheet Dashboard for Data Presentation

Convey all the data you need to present in this one-pager format, an ideal solution tailored for users looking for presentation aids. Global maps, donut chats, column graphs, and text neatly arranged in a clean layout presented in light and dark themes.

Use This Template

2. 3D Column Chart Infographic PPT Template

Represent column charts in a highly visual 3D format with this PPT template. A creative way to present data, this template is entirely editable, and we can craft either a one-page infographic or a series of slides explaining what we intend to disclose point by point.

3. Data Circles Infographic PowerPoint Template

An alternative to the pie chart and donut chart diagrams, this template features a series of curved shapes with bubble callouts as ways of presenting data. Expand the information for each arch in the text placeholder areas.

4. Colorful Metrics Dashboard for Data Presentation

This versatile dashboard template helps us in the presentation of the data by offering several graphs and methods to convert numbers into graphics. Implement it for e-commerce projects, financial projections, project development, and more.

5. Animated Data Presentation Tools for PowerPoint & Google Slides

A slide deck filled with most of the tools mentioned in this article, from bar charts, column charts, treemap graphs, pie charts, histogram, etc. Animated effects make each slide look dynamic when sharing data with stakeholders.

6. Statistics Waffle Charts PPT Template for Data Presentations

This PPT template helps us how to present data beyond the typical pie chart representation. It is widely used for demographics, so it’s a great fit for marketing teams, data science professionals, HR personnel, and more.

7. Data Presentation Dashboard Template for Google Slides

A compendium of tools in dashboard format featuring line graphs, bar charts, column charts, and neatly arranged placeholder text areas. 

8. Weather Dashboard for Data Presentation

Share weather data for agricultural presentation topics, environmental studies, or any kind of presentation that requires a highly visual layout for weather forecasting on a single day. Two color themes are available.

9. Social Media Marketing Dashboard Data Presentation Template

Intended for marketing professionals, this dashboard template for data presentation is a tool for presenting data analytics from social media channels. Two slide layouts featuring line graphs and column charts.

10. Project Management Summary Dashboard Template

A tool crafted for project managers to deliver highly visual reports on a project’s completion, the profits it delivered for the company, and expenses/time required to execute it. 4 different color layouts are available.

11. Profit & Loss Dashboard for PowerPoint and Google Slides

A must-have for finance professionals. This typical profit & loss dashboard includes progress bars, donut charts, column charts, line graphs, and everything that’s required to deliver a comprehensive report about a company’s financial situation.

Overwhelming visuals

One of the mistakes related to using data-presenting methods is including too much data or using overly complex visualizations. They can confuse the audience and dilute the key message.

Inappropriate chart types

Choosing the wrong type of chart for the data at hand can lead to misinterpretation. For example, using a pie chart for data that doesn’t represent parts of a whole is not right.

Lack of context

Failing to provide context or sufficient labeling can make it challenging for the audience to understand the significance of the presented data.

Inconsistency in design

Using inconsistent design elements and color schemes across different visualizations can create confusion and visual disarray.

Failure to provide details

Simply presenting raw data without offering clear insights or takeaways can leave the audience without a meaningful conclusion.

Lack of focus

Not having a clear focus on the key message or main takeaway can result in a presentation that lacks a central theme.

Visual accessibility issues

Overlooking the visual accessibility of charts and graphs can exclude certain audience members who may have difficulty interpreting visual information.

In order to avoid these mistakes in data presentation, presenters can benefit from using presentation templates . These templates provide a structured framework. They ensure consistency, clarity, and an aesthetically pleasing design, enhancing data communication’s overall impact.

Understanding and choosing data presentation types are pivotal in effective communication. Each method serves a unique purpose, so selecting the appropriate one depends on the nature of the data and the message to be conveyed. The diverse array of presentation types offers versatility in visually representing information, from bar charts showing values to pie charts illustrating proportions. 

Using the proper method enhances clarity, engages the audience, and ensures that data sets are not just presented but comprehensively understood. By appreciating the strengths and limitations of different presentation types, communicators can tailor their approach to convey information accurately, developing a deeper connection between data and audience understanding.

If you need a quick method to create a data presentation, check out our  AI presentation maker . A tool in which you add the topic, curate the outline, select a design, and let AI do the work for you.

[1] Government of Canada, S.C. (2021) 5 Data Visualization 5.2 Bar Chart , 5.2 Bar chart .  https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch9/bargraph-diagrammeabarres/5214818-eng.htm

[2] Kosslyn, S.M., 1989. Understanding charts and graphs. Applied cognitive psychology, 3(3), pp.185-225. https://apps.dtic.mil/sti/pdfs/ADA183409.pdf

[3] Creating a Dashboard . https://it.tufts.edu/book/export/html/1870

[4] https://www.goldenwestcollege.edu/research/data-and-more/data-dashboards/index.html

[5] https://www.mit.edu/course/21/21.guide/grf-line.htm

[6] Jadeja, M. and Shah, K., 2015, January. Tree-Map: A Visualization Tool for Large Data. In GSB@ SIGIR (pp. 9-13). https://ceur-ws.org/Vol-1393/gsb15proceedings.pdf#page=15

[7] Heat Maps and Quilt Plots. https://www.publichealth.columbia.edu/research/population-health-methods/heat-maps-and-quilt-plots

[8] EIU QGIS WORKSHOP. https://www.eiu.edu/qgisworkshop/heatmaps.php

[9] About Pie Charts.  https://www.mit.edu/~mbarker/formula1/f1help/11-ch-c8.htm

[10] Histograms. https://sites.utexas.edu/sos/guided/descriptive/numericaldd/descriptiven2/histogram/ [11] https://asq.org/quality-resources/scatter-diagram

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Chapter 3 Presentation of Data

Oct 28, 2014

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Chapter 3 Presentation of Data. Presentation of Data. 1.      Classification and Tabulation Frequency and Cumulative Frequency Tables 2.      Diagrammatic/Graphical Presentation Stem and Leaf Diagram Bar Chart Pareto Chart Pie Chart Histogram Ogive Line Graph Lorenz Curve

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• data values
• frequency polygon
• specialised bar chart
• sectors representing relative magnitude

Presentation Transcript

Chapter 3Presentation of Data

Presentation of Data 1.      Classification and Tabulation • Frequency and Cumulative Frequency Tables 2.      Diagrammatic/Graphical Presentation • Stem and Leaf Diagram • Bar Chart • Pareto Chart • Pie Chart • Histogram • Ogive • Line Graph • Lorenz Curve 3.      Use of Graphs as Management Tool

Stem and Leaf Diagram • A stem and leaf diagram presents a visual summary of a data. • The diagram provides sorting of the data and helps in detecting the distributional pattern of the data.

Classification and Tabulation • Classification is the first step in Tabulation • Classification implies bringing together the items which are similar in some respect(s) • After classification, tabulation is done to condense the data in a compact form which can be easily comprehended

Specific advantages or objectives of Tabulation • It summarises data into rows and columns • It gives appropriate classification with number of data items into cells (intersection of rows and columns), subtotals of rows and columns, etc.This help in drawing useful interpretations about the data • provides significant features of data including comparisons are revealed

Diagrammatic/Graphical Presentation • Stem and Leaf Diagram • Bar Chart • Pareto Chart • Pie Chart • Histogram • Ogive • Line Graph • Lorenz Curve

Bar Chart • It comprises of a series of bars of equal width – the base of the bars being equal to the width of the class interval of a grouped data. • The bars ‘stand’ on a common base line, the heights of the bars being proportional to the frequency of the interval.

Educational Qualification Number of Students B.Tech 55 B.Com 70 B.Sc. 25 B.A. 45 C. A. 20 Bar Chart

Subdivided Bar Chart • A Subdivided Bar chart is a bar chart wherein each bar is divided into further components.

Educational Qualification Metro Large Medium Total B.Tech 15 25 15 55 B.Com 35 20 15 70 B.Sc. 10 10 5 25 B.A. 15 10 20 45 C. A. 10 5 5 20 Subdivided Bar Chart

Percentage Bar Chart • Percentage Bar chart is a bar chart wherein each bar is divided into components which are expressed as percentage of the total bar. • This chart is usually used when we wish to make a visual presentation of comparing the components of various bars which could represent different entities.

Automakers Average Sales Estimates (i) Average Net Profit Estimates (ii) Percentage of Profit to Sales (iii) = (ii)(i) 100 Tata Motors 6,484.80 466 7.2 Hero Honda 2,196.50 224.2 10 Bajaj Auto 2,444.70 345.4 14 TVS Motor 1,032.90 35.1 3.4 Bharat Forge 461.6 63.4 14 Ashok Leyland 1,635.80 94.7 5.8 Percentage Bar Chart

Percentage Bar Chart

Multiple Bar Chart • Multiple bar chart is a bar chart wherein two or more bars are placed together for each entity. • The bars are placed together to give comparative assessment of values of some parameter over two periods of time or at two different locations, etc. • This chart is normally used when we wish to present visual comparision of two year’s data for several entities, brands, etc.

Pain Killer 2005(Rs. in Crores) 2006(Rs. in Crores) Voveran 16.5 23.2 Calpol 13.2 18.2 Nise 15.2 18.6 Combiflam 9.4 14.1 Dolonex 6.8 10.3 Sumo 5.1 7.4 Volini 6.9 9.6 Moov 3.8 4.9 Nimulid 3.5 4.9 Multiple Bar Chart

Multiple Bar Chart

Pareto Chart • This specialised bar chart, named after the famous Italian economist, is used to classify a variable into groups or intervals from largest to smallest frequency. • It facilitates in identification of the most frequent occurrence or causes of an event or phenomenon. It is used for sorting data by using any criteria like geographical regions, organisations like management institutes, banks, countries, cities, etc., and time zones like day/week/month, etc.

Academic Background Frequency Commerce 18 Economics 6 Engineer 17 Information Technology 7 Science 8 Pareto Chart

Pie Chart • It is one of the most popular charts for presenting the ‘whole’ into parts. • It is a circular chart divided into sectors representing relative magnitude of various components.

Sources of Funds Percentage of Total Use of Funds Percentage of Total Excise 17 Central Plan 20 Customs 12 Non-plan Assistance and Expenditure 23 Corporate Tax 21 Defense 12 Income Tax 13 Interest Payments 20 Service Tax 7 States’ Share 18 Borrowings & Others 30 Subsidies 7 Total 100 100 Pie Chart GOVERNMENT OF INDIA’S BUDGET 2007-08

Sources of Funds Percentage of Total * Size of Segment (Degrees) Excise 17 61.2 Customs 12 43.2 Corporate Tax 21 75.6 Income Tax 13 46.8 Service Tax 7 25.2 Borrowings & Others 30 108 Total 100 360 Pie Chart

Use of Funds Percentage of Total Central Plan 20 72 Size of Segment (Degrees) Non-plan Assistance and Expenditure 23 82.8 Defense 12 43.2 Interest Payments 20 72 States’ Share 18 64.8 Subsidies 7 25.2 100 360 Pie Chart

Uses of Funds Central Plan, 20, Subsidies, 7, 9% 24% Interest Payments, 20, 24% Non-plan Defence , 12, 15% Assistance and Expenditure , 23, 28% Pie Chart

Histogram/Frequency Polygon • A histogram comprises of vertical rectangles whose base is proportional to the class interval and height is proportional to the frequency in an interval. • The polygon formed by joining the middle points of the above rectangles is known as the frequency polygon. It gives an idea of the shape of the distribution frequencies of

7 6 6 5 5 4 4 3 3 2 2 1 0 2000 – 3000 3000 – 4000 4000 – 5000 5000 – 6000 6000 – 7000 Equity Holdings in Millions of Rs. Histogram

Frequency Polygon

Ogive • An ogive graph gives an idea about the number of observations less or greater than the values in the range of the variable. • Accordingly, there are two types of ogives, viz. ’Less Than’ and ‘Greater Than’.

Ogive Less than type Greater than type

Line Graph • A line graph is a visual presentation of a set of data values joined by straight lines. • The data values could be over a period of time or over a set of entities like banks, individuals, etc

Bank Business per Emp 05-06 Allahabad Bank 336 153 Andhra Bank 426.75 195.96 Bank of Baroda 396 222.76 Bank of India 381 218.74 Bank of Maharashtra 306.18 191.44 Canara Bank 441.57 214.88 Central Bank of India 240.46 148.77 Corporation Bank 527 290.44 Dena Bank 364 221 Indian Bank 295 156 Indian Overseas Bank 354.73 175.41 Business per Emp 06-07

Line Graph Business per Employee in Banks

Cumulative Percentage of Billionaires Cumulative Equity Holding % of Total Equity Holding 20 16420 18 40 33423 37 60 52135 57 80 71330 78 100 91308 100 Lorenz Curve

120 100 Line of Perfect Equality 80 60 40 20 0 20 40 100 Lorenz Curve

Budgeted • XActual x Business x x x x x x x x x x 80 60 Months M A M J J A S O N D J F Use of Graphs as a Management Tool: A Case Study

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Chapter – 3 Data presentation, analysis and interpretation introduction

This chapter deals the presentation, analysis and interpretation of the data. This chapter consists the general cheracteristictics of the respondents of the study in terms of sex, age, education level, mortial status, work experience, level of in come, occupational status and other current position and the section discuses the main parts of the study. As it was explained in methodology part, the information is gathered from secondary and primary sources especially through distributing questionnaire. Hence, 30uestionains were distributed to the community who live in the town and 20 guestionnaries were distributed to the employees who work in the dilla town numicipality office. In order to acquire information for the study totally 50 questionnaires were distributed. The analysis and interpretation of the finding from the information were approached for a topic on sequentially. In addition to questionnaires, the response towen from secondary data was analyzed. Table and percentage were used present, interpreted data using descriptive type of analysis method. Further more to gather additional data the researcher was held interview with the head of the dilla town municipality office. The respondent personal information This section was designed to indicate that background of the respondants with regards sex, age, sex, educational level, marital status, work experience level of income in the dilla town municipality service taker community. Part I

Business Statistics

S.p.gupta, m.p. gupta, presentation of data - all with video answers.

Chapter Questions

Answer the following questions, each question carries one mark. (i) State the use of pie diagram. (ii) What is the use of histogram ? (iii) What do you mean by a pictogram? (MBA, Madurai Kamraj, Nov. 200I) (iv) Explain how the ogives are drawn for any frequency distribution. (MBA, Madurai Kamraj, Nov. 2003) (v) What is tabulation? (vi) What is a percentile? (vii) What is cumulative frequency curve? (viii) What is open end distribution? (ix) What is histogram? (x) What is frequency polygon? a. Answer the following questions, each question carries four marks. (i) Distinguish between classification and tabulation of data. (MBA, UP Tech. Uniy, 2004) (ii) Give at least two uses each of elassification and tabulation. (iii) Distinguish between discrete and continuous variables with suitable examples. (iv) Distinguish between one dimensional and two dimensional diagrams. (v) What are the important steps in forming a frequency distribution ?

Answer the following questions, each question carries one mark. (d) State the use of pie diagram. (ii) What is the use of histogram ? (iii) What do you mean by a pictogram ? (iv) Explain how the ogives are drawn for any frequency distribution. (MBA, Madurai Kamraj, Nov. 2001) (MBA, Madurai Kamraj, Nov. 2003) (v) What is tabulation? (vi) What is a percentile? (vii) What is cumulative frequency curve? (viii) What is open end distribution? (ix) What is histogram? (x) What is frequency polygon?

Answer the following questions, each question carries four marks. (MBA, UP Tech. Univ, 2004) (i) Distinguish between classification and tabulation of data. (ii) Give at least two uses each of classification and tabulation. (iii) Distinguish between discrete and continuous variables with suitable examples. (iv) Distinguish between one dimensional and two dimensional diagrams. (v) What are the important steps in forming a frequency distribution?

(2) Explain the role of tabulation in presenting business data, and discuss briefly the different methods of presentation.

(a) Explain the role of tabulation in presenting business data, and discuss briefly the different methods of presentation. (9) What are the different types of graphs and charts known to you? What are their uses?

What are the different types of graphs and charts known to you? What are their uses? a) Explain the term 'classification' and 'tabulation'. Point out their importance in a statistical investigation. What precautions would you take in tabulating statistical data?

(a) Explain the term 'classification' and 'tabulation'. Point out their importance in a statistical investigation. What precautions would you take in tabulating statistical data? "In classification and tabulation, commonsense is the chief requisite and experience the chief teacher." Comment. Explain pie diagram and histogram as methods of diagrammatic and graphic presentation of data with suitable examples.

"In classification and tabulation, commonsense is the chief requisite and experience the chief teacher." Comment. (c) Explain pie diagram and histogram as methods of diagrammatic and graphic presentation of data with suitable examples. (a) What are the requisites of a good table? State the rules that serve as a guide in tabulating statistical material.

(a) What are the requisites of a good table? State the rules that serve as a guide in tabulating statistical material. (9) Explain briefly some of the uses of graphs and charts in presenting business data etc. (MBA, Osmania Univ, 2004)

Explain briefly some of the uses of graphs and charts in presenting business data etc. (MBA, Osmania Univ, 2004) a) What are the chief functions of tabulation? What precautions would you take in tabulating statistical data?

(a) What are the chief functions of tabulation? What precautions would you take in tabulating statistical data? (2) What are the characteristics of a good table? (s) Explain Struge's rule in forming frequency distribution.

What are the characteristics of a good table? (s) Explain Struge's rule in forming frequency distribution. a) Distinguish clearly between a continuous variable and a discrete variable. Give two examples of continuous variables and two examples of discontinuous or discrete variables that might be used by a business statistician.

(b) Explain how tables, graphs and charts help in the effective presentation of data. (i) State whether the following statement is true or false :

The heights of rectangles erected on class-intervals are proportional to the cumulative frequency of the classes.

(s) Distinguish clearly between a continuous variable and a discrete variable. Give two examples of continuous variables and two examples of discontinuous or discrete variables that might be used by a business statistician.

Explain how tables, graphs and charts help in the effective presentation of data. (ic) State whether the following statement is true or false : The heights of rectangles erected on class-intervals are proportional to the cumulative frequency of the classes. (a) What are the objections to unequal class-intervals and to open classes? State the conditions under which the use of unequal class-intervals and open classes is desirable and necessary.

(a) What are the objections to unequal class-intervals and to open classes? State the conditions under which the use of unequal class-intervals and open classes is desirable and necessary. Mention the role of tabulation in presenting business data.

Mention the role of tabulation in presenting business data.

Roint out the role of diagrammatic presentation of data. Explain briefly the different types of bar diagrams known to you.

Roint out the role of diagrammatic presentation of data. Explain briefly the different types of bar diagrams known to you. Explain clearly the role and limitations of diagrams and graphs in presenting business data. b) Charts are more effective in attracting attention than any of the other methods of presenting data. Do you agree? Give reasons for your answer.

(a) Explain clearly the role and limitations of diagrams and graphs in presenting business data.

(a) Explain clearly the role and limitations of diagrams and graphs in presenting business data. (5) Charts are more effective in attracting attention than any of the other methods of presenting data. Do you agree? Give reasons for your answer.

(a) -Diagrams do not add anything to the meaning of statistics but when drawn and studied inte!ligently they bring to view the salient characteristics of graph." Explain. (b) Explain briefly the various methods that are used for graphical representation of frequency distributions. (c) Explain the different types of graphs used for representing a frequency distribution. (MBA, KU., 2006)

For a frequency distribution by taking the class-intervals $15-19,20-24$,. etc., for the following data: $$ \begin{array}{lllllllllll} 30 & 42 & 30 & 54 & 40 & 48 & 15 & 17 & 51 & 42 & 25 \\ 41 & 30 & 27 & 42 & 36 & 28 & 26 & 37 & 54 & 44 & 31 \\ 36 & 40 & 36 & 22 & 30 & 31 & 19 & 48 & 16 & 42 & 32 \\ 21 & 22 & 40 & 33 & 41 & 21 & & & & & \end{array} $$

Form a frequency distribution taking a suitable class-interval for the following data giving the age of 52 employees in 2 government agency. $$ \begin{array}{lllllllllll} 67 & 34 & 36 & 48 & 49 & 31 & 61 & 34 & 43 & 45 & 38 \\ 32 & 27 & 61 & 29 & 47 & 36 & 50 & 46 & 30 & 46 & 32 \\ 30 & 33 & 45 & 49 & 48 & 41 & 53 & 36 & 37 & 37 & 47 \\ 30 & 46 & 50 & 28 & 35 & 35 & 38 & 36 & 46 & 43 & 34 \\ 62 & 69 & 50 & 28 & 44 & 43 & 60 & 39 & & & \end{array} $$

Draft a blank table to show : (a) Sex, (b) three ranks - supervisors, assistants and clerks, (c) years 2000 and 2010, and (d) Age groups-18 years and under, over 18 years but less than 55 years, over 55 years.

Prepare a table with a proper title, division and sub-divisions to represent the following heads of information: (i) Export of Cotton piece-goods from India. (ii) To Burma, China, Indonesia, Iran, Iraq. (iii) Amount of piece-goods to each country. (iv) Value of piece-goods to each country. (v) From 2007-08 to 2009-10, year by year. (vi) Total amount of exports each year. (vii) Total value of exports each year.

Represent the following data by a suitable diagram:$$ \begin{array}{lcccccc} \text { Year } & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\ \begin{array}{l} \text { Sale of steel } \\ \text { (in thousand tonnes) } \end{array} & 8 & 8.8 & 9.2 & 10.2 & 7.6 & 12.5 \\ & & & & & & \end{array} $$

Represent the following data by a suitable diagram:$$ \begin{array}{lcccccc} \text { Year } & 2004-2005 & 2005-06 & 2006-07 & 2007-08 & 2008-09 & 2009-10 \\ \text { Profit before taxes } & 28 & 29.4 & 30.2 & 27 & 32.5 & 40.6 \\ \text { (Rs. lakh) } & & & & & & \end{array} $$

$$ \begin{aligned} &\text { Represent the following data by a sub-division bar diagram : }\\ & \end{aligned} $$ $$ \begin{array}{lccc} \text { Year } & 2007-08 & \text { (in lakh for Rs.) } & 2009-10 \\ \text { Gross Income } & 460 & 2008-09 & 552 \\ \text { Gross expenditure } & 400 & 482 & 500 \\ \text { Net Income } & 60 & 450 & 22 \end{array} $$

Represent the following information diagrammatically :$$ \begin{array}{cccccc} \text { Factory } & \begin{array}{c} \text { Wages } \\ (R s .) \end{array} & \begin{array}{c} \text { Material } \\ (R s .) \end{array} & \begin{array}{c} \text { Other costs } \\ (R s .) \end{array} & \begin{array}{c} \text { Profits } \\ (R s .) \end{array} & \text { No. of Units } \\ A & 3,000 & 5,000 & 1,000 & 1,000 & 1,000 \\ B & 2,000 & 3,000 & 800 & 500 & 700 \end{array} $$

Represent the following data by a suitable diagram : UTILIZATION OF 100 PAISE OF INCOME BY XYZ LTD. IN THE YEAR 2009-10 1. Raw Material, Manufacturing and other Expenses 40 Paise 2. Wages, Salaries, Bonus and other Benefits to employees 12 Paise 3. Selling and Distribution Expenses 4 Paise 4. Interest-Financing Charges 4 Paise 5. Depreciation and Development Rebate 3 Paise 6. Excise Duty of Sales 15 Paise 7. Taxation 13 Paise 8. Dividends 6 Paise 9. Surplus retained in Business 3 Paise

Represent the following data by a "Pie Diagram" : CHEQUES CLEARED IN INDIA IN CLEARING HOUSES IN THE YEARS 2009 AND 2010$$ \begin{array}{lrr} \text { Centres } & 2009 & \text { Amount in Crore of rupees } \\ & 829 & 2010 \\ \text { Mumbai } & 1,070 & 2,670 \\ \text { Kolkata } & 108 & 2,443 \\ \text { Chennai } & 313 & 274 \\ \text { Other centres } & 2,320 & 615 \\ \hline \text { Total } & \underline{6,002} \end{array} $$

$$ \begin{aligned} &\text { Draw a suitable diagram for the following : }\\ &\begin{array}{lrr} \text { Expenditure } & \begin{array}{r} \text { Family A } \\ \text { (Income } \end{array} & \begin{array}{r} \text { Family B } \\ \text { (Income } \end{array} \\ \text { Food } & \text { Rs. } 10000) & \text { Rs. } 12000 \text { ) } \\ \text { Clothing } & 3000 & 4000 \\ \text { Education } & 2500 & 2000 \\ \text { Others } & 500 & 3600 \\ \text { Saving or deficit } & 3800 & 3000 \\ \hline \end{array} \end{aligned} $$

Draw the histogram, frequency curve and the ogive curve for the following data pertaining to income distribution for 1500 employees working in a company. $$ \begin{array}{cccc} \begin{array}{c} \text { Monthly income } \\ \text { (in thousand Rs.) } \end{array} & \text { No. of employees } & \begin{array}{c} \text { Monthly income } \\ \text { (in thousand Rs.) } \end{array} & \text { No. of Employees } \\ 18-20 & 10 & 28-30 & 320 \\ 20-22 & 35 & 30-32 & 200 \\ 22-24 & 140 & 32-34 & 75 \\ 24-26 & 300 & 34-36 & 35 \\ 26-28 & 370 & 36-38 & 15 \end{array} $$

What is meant by a histogram? State briefly how it is constructed? Indicate clearly how the histogram in respect of the following data can be drawn (only a rough sketch is required). State also how you can draw histogram in respect of unequal class-intervals.$$ \begin{array}{cccc} \text { Mid-Value } & \text { Frequency } & \text { Mid-value } & \text { Frequency } \\ 115 & 6 & 165 & 60 \\ 125 & 25 & 175 & 38 \\ 135 & 48 & 185 & 22 \\ 145 & 72 & 195 & 3 \end{array} $$

The following table gives the total units produced at the beginning of different years. Represent the data graphically and estimate the mid-year yalue for 2002 and 2010 .$$ \begin{array}{cccc} \text { Years } & \text { Units Produced } & \text { Years } & \text { Units Produced } \\ 2002 & 20 & 2007 & 811 \\ 2003 & 62 & 2008 & 1,104 \\ 2004 & 147 & 2009 & 1,425 \\ 2005 & 300 & 2010 & 1,755 \end{array} $$

Represent the data showing the number of companies in various ranges of subscribed capital by means of a histogram:$$ \begin{array}{cccc} \text { Subscribed capital } & \text { No. of } & \text { Subscribed capital } & \text { No. of } \\ \text { (Rs. crore) } & \text { companies } & \text { (Rs. crore) } & \text { companies } \\ \text { Up to } 10 & 10 & 50-80 & 7 \\ 10-20 & 12 & 80-100 & 8 \\ 20-30 & 10 & \text { Above } 100 & 5 \\ 30-50 & 14 & & \end{array} $$

The data below give the yearly profits (in thousand rupees) of two companies $A$ and $B$ :$$ \begin{array}{ccc} \text { Year } & \text { Company A } & \text { Company B } \\ 2005-06 & 120 & 90 \\ 2006-07 & 135 & 95 \\ 2007-08 & 140 & 108 \\ 2008-09 & 160 & 120 \\ 2009-10 & 175 & 130 \end{array} $$Represent the data by means of a suitable diagram.

Below is given the frequency distribution of weekly wages of 100 workers in a factory: $$ \begin{array}{cccc} \begin{array}{c} \text { Monthly wages } \\ (R s .) \end{array} & \text { No. of workers } & \text { Monthly wages } & \text { No. of workers } \\ 3000-3500 & & (R s .) & \\ 3500-4000 & 3 & 5500-6000 & 10 \\ 4000-4500 & 5 & 6000-6500 & 8 \\ 4500-5000 & 12 & 6500-7000 & 5 \\ 5000-5500 & 23 & 7000-7500 & 3 \end{array} $$ Draw the ogive for the distribution and use it to determine the median wage of a worker.

Present the following information in a suitable tabular form supplying the figures not directly given: "In 2009, out of a total 2,000 workers in a factory 1,550 were members of a trade union. The number of women workens cmployed was 250 , out of which 200 did not belong to any trade union." "In 2010, the number of union workers was 1,725 of which 1,600 were men. The number of non-union workers was 38 among which 155 were women." (MBA, GGSIP Umix)

Draw an Ogive for the following distribution. Read the median from the graph and verify the result by formula. How mas workers eamed monthly wages between Rs. 5,400 and Rs. 5470 ?$$ \begin{array}{cccc} \begin{array}{c} \text { Monthly wages } \\ \text { (in Rs.) } \end{array} & \begin{array}{c} \text { No. of } \\ \text { workers } \end{array} & \begin{array}{c} \text { Monthly wages } \\ \text { (in Rs.) } \end{array} & \begin{array}{c} \text { No. of } \\ \text { workers } \end{array} \\ 5200-5200 & 6 & 5800-6000 & 16 \\ 5400-5400 & 10 & 6000-6200 & 12 \\ 5600-5800 & 22 & 6200-6400 & 15 \end{array} $$

The proprietor of Goodwill Tyres Co. kept a record of the number of car tyres of each brand that were sold during 2009-10 He arranged the data as follows:$$ \begin{array}{lc} \text { Brand } & \text { No. of Tyres Sold } \\ \text { Dunlop } & 280 \\ \text { Modi } & 270 \\ \text { Firestone } & 200 \\ \text { Ceat } & 190 \\ \text { Goodyear } & 160 \\ \text { J.K. } & 100 \end{array} $$ (a) What kind of a distribution is this? (b) What are the class boundaries of each class? (c) Present the data by a suitable diagram/graph.

$$ \begin{aligned} &\text { Draw a suitable diagram to represent the following information : }\\ &\begin{array}{lcc} \text { Selling price } & \text { Company A } & \text { Company B } \\ \text { Raw Materials } & 12,000 & 8,000 \\ \text { Direct Wages } & 5,000 & 6,000 \\ \text { Factory and office on cost } & 4,000 & 3,200 \\ \text { (1,000 } & 800 \end{array} \end{aligned} $$

A company dealing in 60 products, in the course of establishing an inventory control system, to price as shown in the frequency table below : Prepare more than ogive for the distribution on a graph paper. Use this graph to determine 20 th and 80 th percentiles.

Discuss the following terms with illustrations : (i) Classification and Tabulation. (ii) Frequency, cumulative frequency and frequency polygon. (iii) Histogram, line and bar diagrams. (iv) Pie chart. (MBA, Vikram Univ, 1998)

(a) Diagrams help us to visualise the whole meaning of a numerical complex at a single glance". Comment. (b) Draw a suitable diagram to represent the following: $$ \begin{array}{lccccc} & \text { Selling Price } & \text { Qty } & \text { Wages } & \text { Materials } & \text { Others } \\ & \text { Per Unit }(\text { Rs. }) & \text { Sold } & & & \\ \text { Factory A } & 400 & 20 & 3200 & 2400 & 1600 \\ \text { Factory B } & 600 & 30 & 6000 & 6000 & 9000 \end{array} $$ Show also profit or loss as the case may be. (MBA, HPU, 200I)

From the following frequency distribution, prepare the less than and more than cumulative frequency curve (ogive curve) Class-Interval : $0-10$ Frequency : 8 10-20 20-30 30-40 40-50 $\quad 50-60$ (MBA, K.U., 2003)