AP STATS SAPLING: Section 1.3

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. Which set of four numbers has the largest possible standard deviation?

0, 0, 10, 10

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. Which set of four numbers has the smallest possible standard deviation?

1, 1, 1, 1

We all know that fruit is good for us. Here is a histogram of servings of fruit per day claimed by 74 seventeen-year-old girls in a study in Pennsylvania. What is the median number of servings of fruit per day?

2

We all know that fruit is good for us. Here is a histogram of servings of fruit per day claimed by 74 seventeen-year-old girls in a study in Pennsylvania. What is the mean number of servings of fruit per day?

2.62 servings per day

How much storage space does your music use? Below is a dotplot of the file sizes (to the nearest tenth of a megabyte) for 18 randomly selected files on Nathaniel's mp3 player: The distribution of file size has a mean of 𝑥¯x¯ = 3.2 megabytes and a standard deviation of 𝑠𝑥sx = 1.9 megabytes. What is the interquartile range of the file size distribution show in the dotplot?

2.8 mb

Joey's first 14 quiz grades in a marking period were as follows: Suppose Joey has an unexcused absence for the 15th quiz, and he receives a score of 0. What is the range of Joey's first 14 quiz grades? What is the range of Joey's quiz grades after his unexcused absence?

24; 98

The stemplot shows the number of home runs hit by each of the 30 Major League Baseball teams in a single season. Home run totals above what value should be considered outliers?

257

Joey's first 14 quiz grades in a marking period were as follows: Suppose Joey has an unexcused absence for the 15th quiz, and he receives a score of 0. What is the new mean of Joey's quiz grades? What property of the mean does this illustrate?

79.3; This shows that the mean is not resistant to outliers.

To become the President of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 Electoral College votes.Here is a stemplot of the number of electoral votes in 2016 for each of the 50 states and the District of Columbia.

8

Joey's first 14 quiz grades in a marking period were as follows:Suppose Joey has an unexcused absence for the 15th quiz, and he receives a score of 0. What is the new median of Joey's quiz grades? What property of the median does this illustrate?

84; The median is resistant.

Joey's first 14 quiz grades in a marking period were as follows: What is the mean of Joey's quiz grades?

85

Joey's first 14 quiz grades in a marking period were as follows:What is the median of Joey's quiz grades?

85

Consumer Reports magazine rated different types of refrigerators, including those with bottom freezers, those with top freezers, and those with side freezers. One of the variables they measured was annual energy cost (in dollars). The following boxplots show the energy cost distributions for each of these types. Which part of the description of the comparison of the energy cost distributions for the three types of refrigerators is incorrect?

Center: The typical energy cost for the top freezers (median ≈ $85) is greater than the typical cost for the side freezers (median ≈ $75), which is greater than the typical cost for the bottom freezers (median ≈ $69).

To become the President of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 Electoral College votes. Here is a stemplot of the number of electoral votes in 2016 for each of the 50 states and the District of Columbia.

Complete this statement: Because the distribution of the number of electoral votes is skewed to the right , the mean of this distribution is greater than it's median.

According to a study by Nielsen Mobile, "Teenagers ages 13 to 17 are by far the most prolific texters, sending 1742 messages a month."Mr. Williams, a high school statistics teacher, was skeptical about the claims in the article. So he collected data from his first-period statistics class on the number of text messages they had sent in the past 24 hours. Here are the data: Below is a boxplot that displays these results: Do these data seem to support or contradict the magazine's claim? Give statistical evidence to support your answer.

Contradict; 1742 texts a month works out to approximately 58 texts per day. Nearly all of the members of Mr. Williams' class (21 out of 25, to be exact) sent fewer than 58 texts per day.

This is a standard deviation contest. You must choose four numbers from the whole numbers 0 to 10, with repeats allowed. You correctly select number sets with the smallest standard deviation (1, 1, 1, 1) and the largest standard deviation (0, 0, 10, 10). Is it possible to have more than one correct answer for either the smallest or the largest standard deviation number sets? Explain.

For the smallest standard deviation number set, any set of four identical numbers would will have 𝑠𝑥sx = 0, so there are multiple correct answer choices.

The scores on a statistics test had a mean of 81 and a standard deviation of 9. One student was absent on the test day, and his score wasn't included in the calculation. If his score of 84 was added to the distribution of scores, what would happen to the mean and standard deviation?

Mean will increase, and standard deviation will decrease.

To become the president of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 Electoral College votes. Here are a boxplot and some numerical summaries of the electoral vote data: In summarizing the center and variability of the distribution of electoral votes, would it be better to use the median and IQR or the mean and standard deviation? Justify your decision.

Median and IQR because they are resistant measures of center and variability and would not be affected by the outliers in the graph of electoral votes.

Joey's first 14 quiz grades in a marking period were as follows: The range of these 14 scores is 24.Suppose Joey has an unexcused absence for the 15th quiz, and he receives a score of 0. The new range of his scores is now 98. Is the range always the best way to measure the variability for a distribution of quantitative data? Why or why not?

No. The range may not be the best way to describe variability for a distribution of quantitative data because it can be heavily affected by outliers.

The figure displays computer output for data on the amount spent by 50 grocery shoppers.Based only on the computer output, what should you expect the shape of the distribution to be? Explain why

Skewed to the right because the mean is larger than the median.

The figure displays computer output for data on the amount spent by 50 grocery shoppers. Choose the correct interpretation of the standard deviation.

The amount of money spent by these 50 shoppers typically varied by about $21.70 from the mean of $34.70.

How much storage space does your music use? Here is a dotplot of the file sizes (to the nearest tenth of a megabyte) for 18 randomly selected files on Nathaniel's mp3 player: The distribution of file size has a mean of 𝑥¯=3.2x¯=3.2 megabytes and a standard deviation of 𝑠𝑥=1.9sx=1.9 megabytes. Suppose the music file that takes up 7.5 megabytes of storage space is replaced with another version of the file that only takes up 4 megabytes. Suppose the music file that takes up 7.5 megabytes of storage space is replaced with another version of the file that only takes up 4 megabytes. How would this affect the mean and standard deviation?

The mean would decrease and the standard deviation would decrease.

The distribution of file size has a mean of 𝑥¯=3.2x¯=3.2 megabytes and a standard deviation of 𝑠𝑥=1.9sx=1.9 megabytes. Choose the correct interpretation of 𝑠𝑥=1.9sx=1.9 megabytes.

The size of these 18 files typically varies by about 1.9 megabytes from the mean of 3.2 megabytes.

To become the president of the United States, a candidate does not have to receive a majority of the popular vote. The candidate does have to win a majority of the 538 Electoral College votes. Here is a stemplot of the number of electoral votes in 2016 for each of the 50 states and the District of Columbia. Below are a boxplot and some numerical summaries of the electoral vote data. Without doing additional calculations, which of the following is an aspect of this distribution that the stemplot reveals but the boxplot does not?

The stemplot reveals that the distribution has a single peak.

Given the following two distributions:Which has the smaller standard deviation? How do you know?

Variable B has a smaller standard deviation because more of the observations have values closer to the mean than in Variable A's distribution.

Which of the following boxplots best matches the distribution shown in the histogram?

Which of the following boxplots best matches the distribution shown in the histogram? A.

The figure displays computer output for data on the amount spent by 50 grocery shoppers. Which are the correct pair of lower and upper cutoffs for identifying outliers?

lower cutoff = -19.925, upper cutoff = 84.595

If a distribution is skewed to the right with no outliers, which expression is correct?

mean > median