Final Review

How would you describe this graph? 

• Symmetric
• Skewed Right
• Skewed Left
• Bimodal

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CCSS.HSS.ID.A.1

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Your stats teacher tells you your test score was the 3rd quartile for the class.  Which is true?
I. You got a 75% on the test.
II. You can't really tell what this means without knowing the standard deviation.
III. You can't really tell what this means unless the class distribution is nearly normal.

• A. None of these
• B. I only
• C. II only
• D. III only

The advantage of making a stem and leaf display instead of a dotplot is that a stem and leaf plot

• A. Satisfies the area principle
• B. Shows the shape of the distribution better than a dotplot
• C. Preserves the individual data values
• D. A stem and leaf display is for quantitative data, while the dotplot is for categorical data

A reporter collected data on the purchase prices, in thousands of dollars, of 72 cars sold in a region. The above histogram summarizes the reporter’s data.

For a presentation on the data collected, the reporter used the median of the distribution to describe the typical purchase price. Which of the following might explain the use of median to describe the typical purchase price?

• There is an outlier between $80,000 and $85,000. Medians are resistant to outliers, while means are not.

• The number of observations that fall within a given interval is known. However, within each interval, the actual values are not known.

• The distribution is left skewed.

• The values represented in the histogram are in the thousands.

• The distribution is uniform.

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?

1) The median is not likely to change.

2) The range is not likely to change.

3) The mean is likely to increase.

• 1 only

• 3 only

• 1 and 2 only

• 1 and 3 only

• 1, 2 and 3

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CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

The above boxplot summarizes the heights of a group of people who participate in a weekend biking club.

Which of the following statements is supported by the boxplot?

• The mean height is 67 inches.

• The number of people with height at least 70 inches is greater than the number of people with height at most 62 inches.

• The number of people with height at least 67 inches is less than the number of people with height at most 67 inches.

• Approximately 50% of the people have a height between 62 inches and 70 inches.

• Approximately 25% of the people have a height greater than 62 inches.

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CCSS.HSS.ID.A.1

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

The above table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown.

Which of the following statements is supported by the table and boxplot?

• The range of the distribution is 20 years.

• There were 43 people who attended the lecture.

• At least 50% of the people who attended the lecture were 43 years or younger.

• At least 75% of the people who attended the lecture were age 53 years or younger.

• At least 25% of the people who attended the lecture were 33 years old.

The following boxplot summarizes the earnings made on one day at 45 movie theaters. Which of the following best compares the median movie theater earnings with the mean movie theater earnings?

• The median and mean are equal because the distribution is likely symmetric.

• The median and mean are equal because the distribution is likely skewed to the right.

• The median is less than the mean because the distribution is likely symmetric.

• The median is less than the mean because the distribution is likely skewed to the right.

• The median is less than the mean because the distribution is likely skewed to the left.

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CCSS.HSS.ID.A.1

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

Researchers studying catfish estimated the number of fingerling catfish and large catfish living in different rivers throughout the country. The above histograms summarize the relative frequency for each type of catfish.

Based on the histograms, which of the following is the best comparison of the means and the ranges for the two distributions?

• The mean and range of the fingerling catfish are both equal to those of the large catfish.

• The mean and range of the fingerling catfish are both less than those of the large catfish.

• The mean and range of the fingerling catfish are both greater than those of the large catfish.

• The mean of the fingerling catfish is equal to that of the large catfish, and the range of the fingerling catfish is greater than that of the large catfish.

• The mean of the fingerling catfish is equal to that of the large catfish, and the range of the fingerling catfish is less than that of the large catfish.

Independently selected groups of middle-school children were given a poem to memorize. After a certain period of time, they were asked to recall as much of the poem as they could. A back-to-back stem plot of the distribution of the number of words that each group of children could correctly remember is displayed above. Which of the following statements about these data is true?

• There are more students in Group 1 than in Group 2.
• The third quartile of the Group 1 distribution is larger than the maximum value of the Group 2 distribution (that is, 25% of the Group 1 values are larger than any Group 2 value).
• The median of the Group 2 distribution is smaller than the first quartile of the Group 1 distribution (that is, 50% of the Group 2 values are smaller than at least 75% of Group 1 values).
• The mean number of words remembered for Group 1 is smaller than the mean number of words remember for Group 2.

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CCSS.HSS.ID.A.1

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3