chapter 3 presentation of data

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1.3: Presentation of Data

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Skills to Develop

• To learn two ways that data will be presented in the text.

In this book we will use two formats for presenting data sets. The first is a data list, which is an explicit listing of all the individual measurements, either as a display with space between the individual measurements, or in set notation with individual measurements separated by commas.

Example \(\PageIndex{1}\)

The data obtained by measuring the age of \(21\) randomly selected students enrolled in freshman courses at a university could be presented as the data list:

\[\begin{array}{cccccccccc}18 & 18 & 19 & 19 & 19 & 18 & 22 & 20 & 18 & 18 & 17 \\ 19 & 18 & 24 & 18 & 20 & 18 & 21 & 20 & 17 & 19 &\end{array}\]

or in set notation as:

\[ \{18,18,19,19,19,18,22,20,18,18,17,19,18,24,18,20,18,21,20,17,19\} \]

A data set can also be presented by means of a data frequency table, a table in which each distinct value \(x\) is listed in the first row and its frequency \(f\), which is the number of times the value \(x\) appears in the data set, is listed below it in the second row.

Example \(\PageIndex{2}\)

The data set of the previous example is represented by the data frequency table

\[\begin{array}{c|cccccc}x & 17 & 18 & 19 & 20 & 21 & 22 & 24 \\ \hline f & 2 & 8 & 5 & 3 & 1 & 1 & 1\end{array}\]

The data frequency table is especially convenient when data sets are large and the number of distinct values is not too large.

Key Takeaway

• Data sets can be presented either by listing all the elements or by giving a table of values and frequencies.

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Learning Objectives

• To learn two ways that data will be presented in the text.

In this book we will use two formats for presenting data sets. The first is a data list, which is an explicit listing of all the individual measurements, either as a display with space between the individual measurements, or in set notation with individual measurements separated by commas.

Example \(\PageIndex{1}\)

The data obtained by measuring the age of \(21\) randomly selected students enrolled in freshman courses at a university could be presented as the data list:

\[\begin{array}{cccccccccc}18 & 18 & 19 & 19 & 19 & 18 & 22 & 20 & 18 & 18 & 17 \\ 19 & 18 & 24 & 18 & 20 & 18 & 21 & 20 & 17 & 19 &\end{array} \nonumber \]

or in set notation as:

\[ \{18,18,19,19,19,18,22,20,18,18,17,19,18,24,18,20,18,21,20,17,19\} \nonumber \]

A data set can also be presented by means of a data frequency table, a table in which each distinct value \(x\) is listed in the first row and its frequency \(f\), which is the number of times the value \(x\) appears in the data set, is listed below it in the second row.

Example \(\PageIndex{2}\)

The data set of the previous example is represented by the data frequency table

\[\begin{array}{c|cccccc}x & 17 & 18 & 19 & 20 & 21 & 22 & 24 \\ \hline f & 2 & 8 & 5 & 3 & 1 & 1 & 1\end{array} \nonumber \]

The data frequency table is especially convenient when data sets are large and the number of distinct values is not too large.

Key Takeaway

• Data sets can be presented either by listing all the elements or by giving a table of values and frequencies.

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4 Presenting Data

• Published: July 2009
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Data presentation can greatly influence audiences. This chapter reviews principles and approaches for presenting data, focusing on whether data needs to be used. Data can presented using words alone (e.g., metaphors or narratives), numbers (e.g., tables), symbols (e.g., bar charts or line graphs), or some combination that integrates these methods. Although new software packages and advanced techniques are available, visual symbols that can most readily and effectively communicate public health data are pie charts, bar charts, line graphs, icons/icon arrays, visual scales, and maps. Perceptual cues, especially proximity, continuation, and closure, influence how people process information. Contextual cues help enhance meaning by providing sufficient context to help audiences better understand data. Effective data presentation depends upon articulating the purpose for communicating, understanding audiences and context, and developing storylines to be communicated, taking into account the need to present data ethically and in a manner easily understood.

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Presentation of Quantitative Data: Data Visualization

• First Online: 15 December 2018

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We often think of data as being numerical values, and in business, those values are often stated in terms of units of currency (dollars, pesos, dinars, etc.). Although data in the form of currency are ubiquitous, it is quite easy to imagine other numerical units: percentages, counts in categories, units of sales, etc. This chapter, in conjunction with Chap. 3 , discusses how we can best use Excel’s graphic capabilities to effectively present quantitative data ( ratio and interval ) to inform and influence an audience, whether it is in euros or some other quantitative measure. In Chaps. 4 and 5 , we will acknowledge that not all data are numerical by focusing on qualitative ( categorical/nominal or ordinal ) data. The process of data gathering often produces a combination of data types, and throughout our discussions, it will be impossible to ignore this fact: quantitative and qualitative data often occur together. Let us begin our study of data visualization .

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Guerrero, H. (2019). Presentation of Quantitative Data: Data Visualization. In: Excel Data Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-01279-3_2

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Data Presentation

After completing this chapter, you can understand the following:

• The meaning of data classification and its kinds.
• The different methods of condensing the data collected.
• Method of converting the collected data in the form of table.
• Various graphical representations of data and its importance.

3.1 INTRODUCTION

The successful use of data collected depends on the way in which it is arranged, displayed and summarized. As a part of it, this chapter is going to discuss the presentation and condensation of data.

3.2 CLASSIFICATION OF DATA

It is the process of arranging the data based on the similarities and dissimilarities. It is nothing but sorting.

3.2.1 Types of Classification

The data can be classified ...

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Chapter 3: Descriptive Analysis and Presentation of Bivariate Data

Aug 31, 2014

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Chapter 3: Descriptive Analysis and Presentation of Bivariate Data. Chapter Goals. To be able to present bivariate data in tabular and graphic form. To gain an understanding of the distinction between the basic purposes of correlation analysis and regression analysis.

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Presentation Transcript

Chapter Goals • To be able to present bivariate data in tabular and graphic form. • To gain an understanding of the distinction between the basic purposes of correlation analysis and regression analysis. • To become familiar with the ideas of descriptive presentation.

3.1: Bivariate Data Bivariate Data: Consists of the values of two different response variables that are obtained from the same population of interest. Three combinations of variable types: 1. Both variables are qualitative (attribute). 2. One variable is qualitative (attribute) and the other is quantitative (numerical). 3. Both variables are quantitative (both numerical).

Two Qualitative Variables: When bivariate data results from two qualitative (attribute or categorical) variables, the data is often arranged on a cross-tabulation or contingency table. Example: A survey was conducted to investigate the relationship between preferences for television, radio, or newspaper for national news, and gender. The results are given in the table below.

This table may be extended to display the marginal totals (or marginals). The total of the marginal totals is the grand total. Contingency tables often show percentages (relative frequencies). These percentages are based on the entire sample or on the subsample (row or column) classifications.

Percentages based on the grand total (entire sample): The previous contingency table may be converted to percentages of the grand total by dividing each frequency by the grand total and multiplying by 100. For example, 175 becomes 13.3%

These same statistics (numerical values describing sample results) can be shown in a (side-by-side) bar graph.

Percentages based on row (column) totals: The entries in a contingency table may also be expressed as percentages of the row (column) totals by dividing each row (column) entry by that row’s (column’s) total and multiplying by 100. The entries in the contingency table below are expressed as percentages of the column totals. These statistics may also be displayed in a side-by-side bar graph.

One Qualitative and One Quantitative Variable: 1. When bivariate data results from one qualitative and one quantitative variable, the quantitative values are viewed as separate samples. 2. Each set is identified by levels of the qualitative variable. 3. Each sample is described using summary statistics, and the results are displayed for side-by-side comparison. 4. Statistics for comparison: measures of central tendency, measures of variation, 5-number summary. 5. Graphs for comparison: dotplot, boxplot.

Example: A random sample of households from three different parts of the country was obtained and their electric bill for June was recorded. The data is given in the table below. The part of the country is a qualitative variable with three levels of response. The electric bill is a quantitative variable. The electric bills may be compared with numerical and graphical techniques.

Comparison using dotplots: . . : . . . . . . ---+---------+---------+---------+---------+---------+---Northeast . :..:. .. ---+---------+---------+---------+---------+---------+---Midwest . . . . . . : . . ---+---------+---------+---------+---------+---------+---West 24.0 32.0 40.0 48.0 56.0 64.0 The electric bills in the Northeast tend to be more spread out than those in the Midwest. The bills in the West tend to be higher than both those in the Northeast and Midwest.

Comparison using Box-and-Whisker plots:

Two Quantitative Variables: 1. Expressed as ordered pairs: (x, y) 2. x: input variable, independent variable. y: output variable, dependent variable. Scatter Diagram: A plot of all the ordered pairs of bivariate data on a coordinate axis system. The input variable x is plotted on the horizontal axis, and the output variable y is plotted on the vertical axis. Note: Use scales so that the range of the y-values is equal to or slightly less than the range of the x-values. This creates a window that is approximately square.

Example: In a study involving children’s fear related to being hospitalized, the age and the score each child made on the Child Medical Fear Scale (CMFS) are given in the table below. Construct a scatter diagram for this data.

Scatter diagram: age = input variable, CMFS = output variable

3.2: Linear Correlation • Measure the strength of a linear relationship between two variables. • As x increases, no definite shift in y: no correlation. • As x increase, a definite shift in y: correlation. • Positive correlation: x increases, y increases. • Negative correlation: x increases, y decreases. • If the ordered pairs follow a straight-line path: linear correlation.

Example: no correlation. As x increases, there is no definite shift in y.

Example: positive correlation. As x increases, y also increases.

Example: negative correlation. As x increases, y decreases.

Note: 1. Perfect positive correlation: all the points lie along a line with positive slope. 2. Perfect negative correlation: all the points lie along a line with negative slope. 3. If the points lie along a horizontal or vertical line: no correlation. 4. If the points exhibit some other nonlinear pattern: no linear relationship, no correlation. 5. Need some way to measure correlation.

Coefficient of linear correlation: r, measures the strength of the linear relationship between two variables. Pearson’s product moment formula: Note: 1. 2. r = +1: perfect positive correlation 3. r = -1 : perfect negative correlation

Alternate formula for r:

Example: The table below presents the weight (in thousands of pounds) x and the gasoline mileage (miles per gallon) y for ten different automobiles. Find the linear correlation coefficient.

To complete the calculation for r:

Note: 1. r is usually rounded to the nearest hundredth. 2. r close to 0: little or no linear correlation. 3. As the magnitude of r increases, towards -1 or +1, there is an increasingly stronger linear correlation between the two variables. 4. Method of estimating r based on the scatter diagram. Window should be approximately square. Useful for checking calculations.

3.3: Linear Regression • Regression analysis finds the equation of the line that best describes the relationship between two variables. • One use of this equation: to make predictions.

Models or prediction equations: Some examples of various possible relationships. Linear: Quadratic: Exponential: Logarithmic: Note: What would a scatter diagram look like to suggest each relationship?

Method of least squares: Equation of the best-fitting line: Predicted value: Least squares criterion: Find the constants b0 and b1 such that the sum is as small as possible.

Observed and predicted values of y:

The equation of the line of best fit: Determined by b0: slope b1: y-intercept Values that satisfy the least squares criterion:

Example: A recent article measured the job satisfaction of subjects with a 14-question survey. The data below represents the job satisfaction scores, y, and the salaries, x, for a sample of similar individuals. 1. Draw a scatter diagram for this data. 2. Find the equation of the line of best fit.

Preliminary calculations needed to find b1 and b0:

Finding b1 and b0:

Scatter diagram:

Note: 1. Keep at least three extra decimal places while doing the calculations to ensure an accurate answer. 2. When rounding off the calculated values of b0 and b1, always keep at least two significant digits in the final answer. 3. The slope b1 represents the predicted change in y per unit increase in x. 4. The y-intercept is the value of y where the line of best fit intersects the y-axis. 5. The line of best fit will always pass through the point

Making predictions: 1. One of the main purposes for obtaining a regression equation is for making predictions. 2. For a given value of x, we can predict a value of y, 3. The regression equation should be used to make predictions only about the population from which the sample was drawn. 4. The regression equation should be used only to cover the sample domain on the input variable. You can estimate values outside the domain interval, but use caution and use values close to the domain interval. 5. Use current data. A sample taken in 1987 should not be used to make predictions in 1999.

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Robert johnson, patricia kuby, descriptive analysis and presentation of bivariate data - all with video answers.

Bivariate Data

a. Is there a relationship (pattern) between the two variables length of a rainbow trout and weight of a rainbow trout? Explain why or why not. b. Do you think it is reasonable (or possible) to predict the weight of a rainbow trout based on the length of the rainbow trout? Explain why or why not.

a. Is there a relationship between a person's height and shoe size as he or she grows from an infant to age $16 ?$ As one variable gets larger, does the other also get larger? Explain your answers. b. Is there a relationship between height and shoe size for people who are older than 16 years of age? Do taller people wear larger shoes? Explain your answers.

In a national survey of 500 business and 500 leisure travelers, each was asked where he or she would most like "more space."a. Express the table as percentages of the total. b. Express the table as percentages of the row totals. Why might one prefer the table to be expressed this way? c. Express the table as percentages of the column totals. Why might one prefer the table to be expressed this way?

The "In the eye of the beholder" graphic shows two circle graphs, each with four sections. This same information could be represented in the form of a $2 \times 4$ contingency table of two qualitative variables. a. Identify the population and name the two variables. b. Construct the contingency table using entries of percentages based on row totals.

The perfect age" graphic shows the results from a $9 \times 2$ contingency table for one qualitative and one quantitative variable.a. Identify the population and name the qualitative and quantitative variables. b. Construct a bar graph showing the two distributions side by side. c. Does there seem to be a big difference between the genders on this subject?

The National Highway System Designation Act of 1995 allows states to set their own highway speed limits. Most of the states have raised the limits. The November 2008 maximum speed limits on interstate highways (rural) for cars and trucks by each state are given in the following table (in miles per hour):a. Build a cross-tabulation of the two variables vehicle type and maximum speed limit on interstate highways. Express the results in frequencies, showing marginal totals. b. Express the contingency table you derived in part a in percentages based on the grand total. c. Draw a bar graph showing the results from part b. d. Express the contingency table you derived in part a in percentages based on the marginal total for speed limit. e. Draw a bar graph showing the results from part d. If you are using a computer or a calculator, try the cross-tabulation table commands on page 124.

A statewide survey was conducted to investigate the relationship between viewers' preferences for ABC, CBS, NBC, PBS, or FOX for news information and their political party affiliation. The results are shown in tabular form:How many viewers were surveyed?b. Why are these bivariate data? Name the two variables. What type of variable is each one? c. How many viewers preferred to watch CBS? d. What percentage of the survey was Republican? e. What percentage of the Democrats preferred ABC? f. What percentage of the viewers were Republican and preferred PBS?

Consider the accompanying contingency table, which presents the results of an advertising survey about the use of credit by Martan Oil Company customers. a. How many customers were surveyed? b. Why are these bivariate data? What type of variable is each one? c. How many customers preferred to use an oilcompany card? d. How many customers made 20 or more purchases last year? e. How many customers preferred to use an oilcompany card and made between five and nine purchases last year? f. What does the 80 in the fourth cell in the second row mean?

The June 2009 unemployment rates for eastern and western U.S. states were as follows:$$\begin{array}{lcccccc}\hline \text { Eastern } & 8.0 & 10.6 & 10.1 & 7.3 & 9.2 & 11.0 & 12.1 & 7.2 \\\text { Western } & 8.7 & 11.6 & 8.4 & 6.4 & 12.0 & 12.2 & 5.7 & 9.3 \\\hline\end{array}$$.Display these rates as two dotplots using the same scale; compare means and medians.

What effect does the minimum amount have on the interest rate being offered on 3 -month certificates of deposit (CDs)? The following are advertised rates of return, $y,$ for a minimum deposit of $\$ 500, \$ 1000$ $\$ 2500, \$ 5000,$ or $\$ 10,000, x .$ (Note that $x$ is in $\$ 100$ and $y$ is annual percentage rate of return.)$$\begin{array}{cc|cc|cc} \text { Min Deposit } & \text { Rate } & \text { Min Deposit } & \text { Rate } & \text { Min Deposit } & \text { Rate } \\\hline 100 & 0.95 & 25 & 1.00 & 25 & 0.75 \\100 & 1.24 & 50 & 1.00 & 10 & 0.75 \\10 & 1.24 & 100 & 1.00 & 100 & 0.70 \\10 & 1.15 & 5 & 1.00 & 5 & 0.64 \\100 & 1.10 & 10 & 1.00 & 10 & 0.50 \\50 & 1.09 & 10 & 0.80 & 100 & 0.35 \\100 & 1.07 & 10 & 0.75 & 25 & 0.35 \\ 5 & 1.00 & 10 & 0.75 & 5 & 0.99 \\25 & 0.75 & & & & \\\hline\end{array}$$.a. Prepare a dotplot of the five sets of data using a common scale. b. Prepare a 5 -number summary and a boxplot of the five sets of data. Use the same scale for the boxplots. c. Describe any differences you see among the three sets of data.

Can a woman's height be predicted from her mother's height? The heights of some mother-daughter pairs are listed; $x$ is the mother's height and $y$ is the daughter's height.$$\begin{array}{l|llllllllll}\hline x & 63 & 63 & 67 & 65 & 61 & 63 & 61 & 64 & 62 & 63 \\y & 63 & 65 & 65 & 65 & 64 & 64 & 63 & 62 & 63 & 64 \\\hline\end{array}$$,$$\begin{array}{l|lllllllllll} \hline \boldsymbol{x} & 64 & 63 & 64 & 64 & 63 & 67 & 61 & 65 & 64 & 65 & 66 \\ \boldsymbol{y} & 64 & 64 & 65 & 65 & 62 & 66 & 62 & 63 & 66 & 66 & 65 \\\hline\end{array}$$. a. Draw two dotplots using the same scale and showing the two sets of data side by side. b. What can you conclude from seeing the two sets of heights as separate sets in part a? Explain. c. Draw a scatter diagram of these data as ordered pairs. d. What can you conclude from seeing the data presented as ordered pairs? Explain.

The following tables list the ages, heights (in inches), and weights (in pounds) of the players on the 2009 roster for the National Hockey League teams Boston Bruins and Edmonton Oilers.a. Compare each of the three variables-height, weight, and age - using either a dotplot or a histogram (use the same scale). b. $\quad$ Based on what you see in the graphs in part a, can you detect a substantial difference between the two teams in regard to these three variables? Explain. c. Explain why the data, as used in part a, are not bivariate data.

Consider the two variables of a person's height and weight. Which variable, height or weight, would you use as the input variable when studying their relationship? Explain why.

Draw a coordinate axis and plot the points (0,6) $(3,5),(3,2),$ and (5,0) to form a scatter diagram. Describe the pattern that the data show in this display.

Does studying for an exam pay off? a. Draw a scatter diagram of the number of hours studied, $x,$ compared with the exam grade received, $y$.$$\begin{array}{l|rrrrr}\hline \boldsymbol{x} & 2 & 5 & 1 & 4 & 2 \\ \boldsymbol{y} & 80 & 80 & 70 & 90 & 60 \\\hline\end{array}$$.b. Explain what you can conclude based on the pattern of data shown on the scatter diagram drawn in part a. (Retain these solutions to use in Exercise $3.55,$ p. 157 )

Americans Love Their Automobiles" (Applied Example 3.4 on p. 128) to answer the following questions: a. Name the two variables used. b. Does the scatter diagram suggest a relationship between the two variables? Explain. c. What conclusion, if any, can you draw from the appearance of the scatter diagram?

Growth charts are commonly used by a child's pediatrician to monitor a child's growth. Consider the growth chart that follows.a. What are the two variables shown in the graph? b. What information does the ordered pair (3,87) represent?an two c. Describe how the pediatrician might use this chart and when what types of conclusions might be based on the information displayed by it.

Draw a scatter diagram showing height, $x,$ and weight, $y,$ for the Boston Bruins hockey team, using the data in Exercise 3.12 7d se b. Draw a scatter diagram showing height, $x,$ and $\Rightarrow ? \quad$ weight, $y,$ for the Edmonton Oilers hockey team using the data in Exercise 3.12 5), c. Explain why the data, as used in parts a and b, are n. bivariate data.

The accompanying data show the number of hours, $x,$ studied for an exam and the grade 50 received, $y(y \text { is measured in tens; that is, } y=8$ means that the grade, rounded to the nearest 10 points, is 80 ). Draw the scatter diagram. (Retain this solution to use in Exercise $3.37,$ p. $143 .$ )

An experimental psychologist asserts that the older a child is, the fewer irrelevant answers he or she will give during a controlled experiment. To investigate this claim, the following data were collected. Draw a scatter diagram. (Retain this solution to use in Exercise $3.38, p .143 .)$. $$\begin{array}{l|rrrrrrrrrr}\hline \text { Age, } x & 2 & 4 & 5 & 6 & 6 & 7 & 9 & 9 & 10 & 12 \\ \text { Irr Answers, } y & 12 & 13 & 9 & 7 & 12 & 8 & 6 & 9 & 7 & 5 \\\hline\end{array}$$.

A sample of 15 upper-class students whe commute to classes was selected at registration. They were asked to estimate the distance $(x)$ and the time $(y)=$ required to commute each day to class (see the following table).$$\begin{array}{cc|cc}\begin{array}{c}\text { Distance, } x \\\text { (nearest mile) }\end{array} & \begin{array}{c}\text { Time, } y \\\text { (nearest }5 \text { minutes }) \end{array} & \begin{array}{c}\text { Distance, } x \\\text { (nearest mile) }\end{array} & \begin{array}{c}\text { Time, } y \\\text { (nearest } 5 \text { minutes } \end{array} \\\hline 18 & 20 & 2 & 5 \\8 & 15 & 15 & 25 \\20 & 25 & 16 & 30 \\5 & 20 & 9 & 20 \\5 & 15 & 21 & 30 \\11 & 25 & 5 & 10 \\9 & 20 & 15 & 20 \\10 & 25 & & \\\hline \end{array}$$.a. Do you expect to find a linear relationship between the two variables commute distance and commute time? If so, explain what relationship you expect. b. Construct a scatter diagram depicting these data. c. Does the scatter diagram in part b reinforce what you expected in part a?

Refer to the 2009 4-wheel-drive, 6-cylinder SUVs chart in Applied Example 3.4 on page 128 and the two variables gas tank capacity, $x,$ and the cost to fill it, $y$ a. If you were to draw scatter diagrams of these two variables, on the same graph but separate, for the SUVs that use regular and premium gasoline, do you think the two sets of data would be distinguishable? Explain what you anticipate seeing. b. Construct a scatter diagram of tank capacity, $x,$ and fill-up cost, $y,$ for the SUVs using regular gasoline. c. Construct a scatter diagram of tank capacity, $x,$ and fill-up cost, $y,$ for the SUVs using premium gasoline on the scatter diagram for part b. d. Are the two sets of data distinguishable? e. How does your answer in part a compare to your answer in part d? Explain any difference.

Baseball stadiums vary in age, style and size, and many other ways. Fans might think of the size of a stadium in terms of the number of seats, while players might measure the size of a stadium in terms of the distance from home plate to the centerfield fence.$$\begin{array}{ll|cc|cc}\text { Seats } & \text { CF } & \text { Seats } & \text { CF } & \text { Seats } & \text { CF } \\\hline 38,805 & 420 & 36,331 & 434 & 40,950 & 435 \\41,118 & 400 & 43,405 & 405 & 38,496 & 400 \\56,000 & 400 & 48,911 & 400 & 41,900 & 400 \\45,030 & 400 & 50,449 & 415 & 42,271&404 \\34,077 & 400 & 50,091 & 400 & 43,647 & 401 \\40,793 & 400 & 43,772 & 404 & 42,600 & 396 \\56,144 & 408 & 49,033 & 407 & 46,200 & 400 \\50,516 & 400 & 47,447 & 405 & 41,222 & 403 \\40,615 & 400 & 40,120 & 422 & 52,355 & 408 \\48,190 & 406 & 41,503 & 404 & 45,000 & 408 \\\hline\end{array}$$.Is there a relationship between these two measurements of the "size" of the 30 Major League Baseball stadiums? a. What do you think you will find? Bigger fields have more seats? Smaller fields have more seats? No relationship between field size and number of seats? A strong relationship between field size and number of seats? Explain. b. Construct a scatter diagram. c. Describe what the scatter diagram tells you, including a reaction to your answer in part a.

Most adult Americans drive. But do you have any idea how many licensed drivers there are in each U.S. state? The table here lists the number of male and female drivers licensed in each of 15 randomly selected U.S. states during 2007 $$\begin{array}{lcccc} \hline \text { Male } & \text { Femole } & \text { Male } & \text { Female } \\ \hline 17.92 & 17.10 & 59.07 & 54.62 \\5.18 & 5.10 & 2.38 & 2.33 \\21.24 & 21.85 & 15.01 & 16.26 \\10.03 & 10.15 & 75.98 & 75.86 \\14.52 & 14.82 & 8.32 & 8.20 \\15.91 & 15.59 & 25.26 & 23.53 \\3.74 & 3.62 & 2.05 & 1.93 \\6.77 & 6.89 & & \\\hline\end{array}$$.a. Do you expect to find a linear (straight-line) relationship between number of male and number of female licensed drivers per state? How strong do you anticipate this relationship to be? Describe. b. Construct a scatter diagram using $x$ for the number of male drivers and $y$ for the number of female drivers. c. Compare the scatter diagram to your expectations in part a. How did you do? Explain. d. Are there data points that look like they are separate from the pattern created by the rest of ordered pairs? If they were removed from the dataset, would the results change? What caused these point(s) to be separate from the others, but yet still be part of the extended pattern? Explain. e. Use the dataset for all 51 states to construct a scatter diagram. Compare the pattern of the sample of 15 to the pattern shown by all $51 .$ Describe in detail. f. Did the sample provide enough information for you to understand the relationship between the two variables in this situation? Explain.

Ronald Fisher, an English statistician $(1890-1962),$ collected measurements for a sample of 150 irises. Of concern were five variables: species, petal width (PW), petal length (PL), sepal width (SW), and sepal length (SL) (all in $\mathrm{mm}$ ). Sepals are the outermost leaves that encase the flower before it opens. The goal of Fisher's experiment was to produce a simple function that could be used to classify flowers correctly. A random sample of his complete data set is given in the accompanying table.a. Construct a scatter diagram of petal length, $x,$ and petal width, $y .$ Use different symbols to represent the three species.. b. Construct a scatter diagram of sepal length, $x,$ and sepal width, $y .$ Use different symbols to represent the three species. c. Explain what the scatter diagrams in parts a and b portray.

Total solar eclipses actually take place nearly as often as total lunar eclipses, but the former are visible over a much narrower path. Both the path width and the duration vary substantially from one eclipse to the next. The table below shows the duration (in seconds) and path width (in miles) of 44 total solar eclipses measured in the past and those projected to the year 2010 :a. Draw a scatter diagram showing duration, $y,$ and path width, $x,$ for the total solar eclipses. b. How would you describe this diagram? c. The durations and path widths for the years $2006-2009$ were projections. The recorded values were:Compare the recorded values to the projections. Comment on accuracy. $$\begin{array}{lll} \text { Year } & \text { Path Width } & \text { Duration } \\ \hline 2006 & 65 \text { miles } & 247 \text { sec } \\ 2008 & 147 \text { miles } & 147 \text { sec } \\ 2009 & 160 \text { miles } & 399 \text { sec } \end{array}$$.Compare the recorded values to the projections. Comment on accuracy.

Google Cloud Next 2024: Everything announced so far

Google’s Cloud Next 2024 event takes place in Las Vegas through Thursday, and that means lots of new cloud-focused news on everything from Gemini, Google’s AI-powered chatbot , to AI to devops and security. Last year’s event was the first in-person Cloud Next since 2019, and Google took to the stage to show off its ongoing dedication to AI with its Duet AI for Gmail and many other debuts , including expansion of generative AI to its security product line and other enterprise-focused updates and debuts .

Don’t have time to watch the full archive of Google’s keynote event ? That’s OK; we’ve summed up the most important parts of the event below, with additional details from the TechCrunch team on the ground at the event. And Tuesday’s updates weren’t the only things Google made available to non-attendees — Wednesday’s developer-focused stream started at 10:30 a.m. PT .

Google Vids

Leveraging AI to help customers develop creative content is something Big Tech is looking for, and Tuesday, Google introduced its version. Google Vids, a new AI-fueled video creation tool , is the latest feature added to the Google Workspace.

Here’s how it works: Google claims users can make videos alongside other Workspace tools like Docs and Sheets. The editing, writing and production is all there. You also can collaborate with colleagues in real time within Google Vids. Read more

Gemini Code Assist

After reading about Google’s new Gemini Code Assist , an enterprise-focused AI code completion and assistance tool, you may be asking yourself if that sounds familiar. And you would be correct. TechCrunch Senior Editor Frederic Lardinois writes that “Google previously offered a similar service under the now-defunct Duet AI branding.” Then Gemini came along. Code Assist is a direct competitor to GitHub’s Copilot Enterprise. Here’s why

And to put Gemini Code Assist into context, Alex Wilhelm breaks down its competition with Copilot, and its potential risks and benefits to developers, in the latest TechCrunch Minute episode.

Google Workspace

Image Credits: Google

Among the new features are voice prompts to kick off the AI-based “Help me write” feature in Gmail while on the go . Another one for Gmail includes a way to instantly turn rough email drafts into a more polished email. Over on Sheets, you can send out a customizable alert when a certain field changes. Meanwhile, a new set of templates make starting a new spreadsheet easier. For the Doc lovers, there is support for tabs now. This is good because, according to the company, you can “organize information in a single document instead of linking to multiple documents or searching through Drive.” Of course, subscribers get the goodies first. Read more

Google also seems to have plans to monetize two of its new AI features for the Google Workspace productivity suite. This will look like $10/month/user add-on packages. One will be for the new AI meetings and messaging add-on that takes notes for you, provides meeting summaries and translates content into 69 languages. The other is for the introduced AI security package, which helps admins keep Google Workspace content more secure. Read more

In February, Google announced an image generator built into Gemini, Google’s AI-powered chatbot. The company pulled it shortly after it was found to be randomly injecting gender and racial diversity into prompts about people. This resulted in some offensive inaccuracies. While we waited for an eventual re-release, Google came out with the enhanced image-generating tool, Imagen 2 . This is inside its Vertex AI developer platform and has more of a focus on enterprise. Imagen 2 is now generally available and comes with some fun new capabilities, including inpainting and outpainting. There’s also what Google’s calling “text-to-live images” where you  can now create short, four-second videos from text prompts, along the lines of AI-powered clip generation tools like Runway ,  Pika  and  Irreverent Labs . Read more

Vertex AI Agent Builder

We can all use a little bit of help, right? Meet Google’s Vertex AI Agent Builder, a new tool to help companies build AI agents.

“Vertex AI Agent Builder allows people to very easily and quickly build conversational agents,” Google Cloud CEO Thomas Kurian said. “You can build and deploy production-ready, generative AI-powered conversational agents and instruct and guide them the same way that you do humans to improve the quality and correctness of answers from models.”

To do this, the company uses a process called “grounding,” where the answers are tied to something considered to be a reliable source. In this case, it’s relying on Google Search (which in reality could or could not be accurate). Read more

Gemini comes to databases

Google calls Gemini in Databases a collection of features that “simplify all aspects of the database journey.” In less jargony language, it’s a bundle of AI-powered, developer-focused tools for Google Cloud customers who are creating, monitoring and migrating app databases. Read more

Google renews its focus on data sovereignty

Image Credits: MirageC / Getty Images

Google has offered cloud sovereignties before, but now it is focused more on partnerships rather than building them out on their own. Read more

Security tools get some AI love

Image Credits: Getty Images

Google jumps on board the productizing generative AI-powered security tool train with a number of new products and features aimed at large companies. Those include Threat Intelligence, which can analyze large portions of potentially malicious code. It also lets users perform natural language searches for ongoing threats or indicators of compromise. Another is Chronicle, Google’s cybersecurity telemetry offering for cloud customers to assist with cybersecurity investigations. The third is the enterprise cybersecurity and risk management suite Security Command Center. Read more

Nvidia’s Blackwell platform

One of the anticipated announcements is Nvidia’s next-generation Blackwell platform coming to Google Cloud in early 2025. Yes, that seems so far away. However, here is what to look forward to: support for the high-performance Nvidia HGX B200 for AI and HPC workloads and GB200 NBL72 for large language model (LLM) training. Oh, and we can reveal that the GB200 servers will be liquid-cooled. Read more

Chrome Enterprise Premium

Meanwhile, Google is expanding its Chrome Enterprise product suite with the launch of Chrome Enterprise Premium . What’s new here is that it mainly pertains mostly to security capabilities of the existing service, based on the insight that browsers are now the endpoints where most of the high-value work inside a company is done. Read more

Gemini 1.5 Pro

Everyone can use a “half” every now and again, and Google obliges with Gemini 1.5 Pro. This, Kyle Wiggers writes, is “Google’s most capable generative AI model,” and is now available in public preview on Vertex AI, Google’s enterprise-focused AI development platform. Here’s what you get for that half: T he amount of context that it can process, which is from 128,000 tokens up to 1 million tokens, where “tokens” refers to subdivided bits of raw data (like the syllables “fan,” “tas” and “tic” in the word “fantastic”). Read more

Open source tools

At Google Cloud Next 2024, the company debuted a number of open source tools primarily aimed at supporting generative AI projects and infrastructure. One is Max Diffusion, which is a collection of reference implementations of various diffusion models that run on XLA, or Accelerated Linear Algebra, devices. Then there is JetStream, a new engine to run generative AI models. The third is MaxTest, a collection of text-generating AI models targeting TPUs and Nvidia GPUs in the cloud. Read more

We don’t know a lot about this one, however, here is what we do know : Google Cloud joins AWS and Azure in announcing its first custom-built Arm processor, dubbed Axion. Frederic Lardinois writes that “based on Arm’s Neoverse 2 designs, Google says its Axion instances offer 30% better performance than other Arm-based instances from competitors like AWS and Microsoft and up to 50% better performance and 60% better energy efficiency than comparable X86-based instances.” Read more

The entire Google Cloud Next keynote

If all of that isn’t enough of an AI and cloud update deluge, you can watch the entire event keynote via the embed below.

Google Cloud Next’s developer keynote

On Wednesday, Google held a separate keynote for developers . They offered a deeper dive into the ins and outs of a number of tools outlined during the Tuesday keynote, including Gemini Cloud Assist, using AI for product recommendations and chat agents, ending with a showcase from Hugging Face. You can check out the full keynote below.