Comparing Data Sets

Practice Problem 1:

The histogram represents the daily low and high temperatures in a city during March.

Which comparison of the distributions is true?

• The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is nearly symmetric.

• The distribution of low temperatures is skewed right, and the distribution of high temperatures is nearly symmetric.

• The distribution of low temperatures is nearly symmetric, and the distribution of high temperatures is skewed right.

• The distribution of low temperatures is skewed right, and the distribution of high temperatures is skewed right.

Practice Problem 2:

Ms. Barnsley separates her class into two groups. She gives each student the same 25-question math quiz. Group A uses a calculator, while Group B does not. The table shows the completion times, in minutes, of students in each group.

Which statement is true about the distributions of completion times?

• The students in Group A tended to complete the quiz in less time.

• The median of Group A is greater than the median of Group B.

• The means of both groups are about the same.

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

Practice Problem 3:

The histogram represents the distributions of rain amounts in two cities.

Which best explains how the histogram is useful for comparing the shapes of the data sets?

• It is easier to visually compare the means of the data.

• It is easier to visually compare the standard deviations of the data.

• It is easier to visually compare the medians of the data.

• It is easier to visually compare symmetry and skew of the data.

Practice Problem 4:

The table shows the number of pages in the books in Box A and the number of pages in the books in Box B.

Which statement is true about the data?

• The mean of Box A is greater than the mean of Box B.

• The mean of Box B is greater than the mean of Box A.

• The median of Box A is greater than the median of Box B.

• The median of Box B is greater than the median of Box A.

The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale.

What is the difference of the medians?

A research study was conducted to measure the time students focus on a task before being distracted. The box plots show the distributions of attention spans of high school and college students.

Which statements are true regarding the data sets? Select two options.

• The median attention span of college students is greater than the median attention span of high school students. 

• The range of attention span of college students is greater than the range of attention spans of high school students.

• The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students.

• All of the college students in the study had greater attention spans than the high school students.

• The minimum attention span of high school students is greater than the minimum attention span of college students.

The box plots represent the distributions of typing speeds of students before and after a computer-programming course.

Which statement is true about the variability of the distributions?

• The interquartile range of the typing speeds after the course is greater than the interquartile range of the speeds before the course.

• The interquartile ranges of the two distributions are the same.

• The range of the speeds after the course is smaller than the range of the speeds before the course.

• The ranges of the two distributions are the same.

The histogram shows the distributions of essay scores for high school sophomores and juniors in a contest.

Which comparison of the distributions is true?

• Both distributions are nearly symmetric.

• Both distributions are right-skewed.

• The distribution of sophomores’ scores is right-skewed, and the distribution of juniors’ scores is left-skewed.

• The distribution of sophomores’ scores is left-skewed, and the distribution of juniors’ scores is right-skewed.

The table shows the growth, in centimeters, of plants in two different soils after two weeks.

Which statement explains which soil tended to have a greater growth?

• Soil A had greater growth because its data have a greater standard deviation.

• Soil A had greater growth because its data have a greater mean.

• Soil B had greater growth because its data have a greater interquartile range.

• Soil B had greater growth because its data have a greater median.

The box plots represent the ages of pennies in two 50-cent rolls.

By looking at the plots, Beth says that the two means are about 5 years apart. Which is true about Beth’s statement?

• She is correct because the medians are 10 years apart, which means the means are half of that, or 5 years apart.

• She is correct because the maximum ages of the pennies in each set are 5 years apart.

• She is not correct because the means are both equal to 12.

• She may not be correct because means cannot be determined from the box plots.