STATS 1.7-1.9

A school is having a contest in which students guess the number of candies in a jar. The student whose guess is closest to the correct number of candies in the jar wins a prize. The number of candies guessed by male and female students is shown in the back-to-back stemplot.

Which of the following statements is true about the distributions of guesses?

• The distribution of guesses for male students is skewed to the left, and the distribution of guesses for female students is skewed to the right.

• The distribution of guesses for male students is skewed to the right, and the distribution of guesses for female students is skewed to the left.

• The distributions of guesses for male and female students are both skewed to the right.

• The distributions of guesses for male and female students are both skewed to the left.

• The distributions of guesses for male and female students are both symmetric.

Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots.

Which of the following statements is true?

• The range in the amount of time in minutes males in the sample of customers spent in the store is approximately 40 minutes.

• The mean amount of time in minutes males in the sample of customers spent in the store is approximately 20 minutes.

• The third quartile of the amount of time in minutes males in the sample of customers spent in the store is approximately 45 minutes.

• The interquartile range of the amount of time in minutes females in the sample of customers spent in the store is 15 minutes.

• Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers.

In a standard golf tournament, golfers play 18 holes of golf on each of 4 consecutive days. For each hole, golfers keep track of the number of times they hit the ball (strokes) before the ball goes into the cup. A golfer’s score for the tournament is the total number of strokes needed to complete the tournament. The boxplots below summarize the scores for golfers who competed in tournament 1 and golfers who competed in tournament 2.

Based on the boxplots, which of the following statements must be true?

• More golfers played in tournament 1 than in tournament 2.

• In both tournaments, at least half the golfers completed the tournament with a score less than 288.

• The number of golfers who completed tournament 1 with a score less than 288 was greater than the number of golfers who completed tournament 2 with a score less than 288.

• The range of scores for tournament 1 is less than the range of scores for tournament 2

• The score of the golfer with the least score in tournament 1 was greater than the score of the golfer with the least score in tournament 2.

A car rental agency has two locations in a city. The boxplots below summarize the miles driven for one day of single-day car rentals at each location.

Based on the boxplots, which statement provides the best comparison of the two locations?

• The number of single-day rentals is greater for location A than for location B.

• The number of single-day rentals is less for location A than for location B.

• Compared with location A, the miles driven for location B display more variability, and the median is greater.

• Compared with location A, the miles driven for location B display less variability, and the median is greater.

• Compared with location A, the miles driven for location B display less variability, and the median is about the same.

Which of the following statements must be true about the data sets A and B displayed in the histograms?

• The mean of data set A is equal to the mean of data set B.

• The median of data set A is equal to the median of data set B

• The range of data set A is equal to the range of data set B.

• The standard deviation of data set A is less than the standard deviation of data set B.

• The standard deviation of data set A is greater than the standard deviation of data set B.

A sociologist collected data from a sample of people on their highest level of education and the number of times they visited any fast food restaurant during the previous week. The data are summarized in the boxplots.

Based on the boxplots, which of the following statements must be true?

• The number of people surveyed at the more than four-year college level is greater than the number of people surveyed at the high school level.

• The proportion of people surveyed from the first quartile to the third quartile at the four-year college level is less than the respective proportion at the community college level.

• The interquartile range (IQR) for the number of visits at the more than four-year college level is less than the IQR for the number of visits at the community college level.

• The maximum number of visits at the community college level is greater than the maximum number of visits at the high school level.

• The median number of visits at the four-year college level is greater than the median number of visits at the high school level

Nutritionists examined the sodium content of different brands of potato chips. Each brand was classified as either healthy or regular based on how the chips were marketed to the public. The sodium contents, in milligrams (mg) per serving, of the chips are summarized in the boxplots,

Based on the boxplots, which statement gives a correct comparison between the two classifications of the sodium content of the chips?

• The number of brands classified as healthy is greater than the number of brands classified as regular.

• The interquartile range (IQR) of the brands classified as healthy is greater than the IQR of the brands classified as regular.

• The range of the brands classified as healthy is less than the range of the brands classified as regular.

• • 
    

    The median of the brands classified as healthy is more than twice the median of the brands classified as regular.

• The brand with the least sodium content and the brand with the greatest sodium content are both classified as healthy.

The figure summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center for environmental study. Approximately half of the trees were fertilized yearly, and the remaining trees were never fertilized. Which of the following statements about the medians and interquartile ranges (IQRs) of the heights of the two groups of trees 6 years after being planted is true?

• The medians and IQRs are the same for the unfertilized trees and the fertilized trees.

• The median for the unfertilized trees is greater than the median for the fertilized trees, and the IQR is also greater for the unfertilized trees.

• The median for the unfertilized trees is the same as the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

• The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

• The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is less for the unfertilized trees.

A random sample of 374 United States pennies was collected, and the age of each penny was determined. According to the boxplot, what is the approximate interquartile range (IQR) of the ages?

• 10

• 12

• 16

• 20

• 8

The histogram shows the distribution of heights, in inches, of 100 adult men.

Based on the histogram, which of the following is closest to the interquartile range, in inches, of the distribution?

• 2

• 5

• 9

• 12

• 15