Center and Variability Comparing

The box-and-whisker plots below show the scores earned by 6th and 7th graders on a year-end reading test. Which statement is best supported by the box-and-whisker plots?

• The range of the 7^th grade scores is greater than the range of the 6^th grade scores.

• The median of the 6^th grade scores is greater than the median of the 7^th grade scores.

• The mean of the 7^th grade scores is less than the mean of the 6^th grade scores.

• The number of 6^th graders who took the test is greater than the number of 7^th graders who took the test.

The ages of the starting players of two soccer teams are shown below. Based on this data, select all the true statements below.

• The median of ages on the Knights team is greater than the median of ages on the Trojans team.

• The mean of the ages on the Knights team is greater than the median of the ages on the Trojans team.

• The median of ages on the Knights team is one greater than the range of ages on the Trojans team.

• The mean of the ages on the Knights team is less than the mean of the ages on the Trojans team.

• The mean of the ages on the Knights team is greater than the mean of the ages on the Trojans team.

The dot plots below show the number of customers at Mr. Burger and Mr. Chicken during rush hour over the course of 10 days. Which statement correctly compares the distribution of the number of customers at each restaurant during rush hour?

• Mr. Burger's number of customers during rush hour, is greater than Mr. Chicken's number of customers during rush hour.

• Mr. Burger's median number of customers during rush hour, is greater than Mr. Chicken's median number of customers during rush hour.

• There is more variability in Mr. Chicken's number of customers during rush hour, than Mr. Burger's number of customers during rush hour.

• There is less variability in Mr. Chicken's number of customers during rush hour, than Mr. Burger's number of customers during rush hour.

The data below shows the scores of two groups of ten students on a math quiz and a science quiz.

Math: 72, 92, 88, 67, 54, 58, 64, 76, 65, 72

Science: 84, 78, 56, 89, 54, 68, 75, 78, 84, 60

Based on the data, which statements are true?

• The median score was greater for math, but the variability was greater for science.

• The median score was greater for science, but the variability was greater for math.

• Both the median score and variability for the math scores are less than that of the science scores.

• Both the median score and variability of the math scores are greater than that of the science scores.

• The range for science is less than the range for math.

The box and whisker plots below, illustrate the scores earned by 2 biology classes on a recent test. Select all statements that are supported by the plots above.

• The range of the 3^rd period scores is less than the range of the 5^th period scores.

• The median of the 5^th period scores is greater than the median of the 3^rd period scores.

• The number of students who took the test is larger in the 5^th period class than in the 3^rd period class.

• The interquartile range is the same for both classes.

• The 3^rd period class has a higher median but has a lower range than the 5^th period class.

Given the following distributions, which has the smallest IQR?

• Red

• Purple

• Black

Given the following distributions, which has the highest median?

• Red

• Purple

• Black

Gabriella’s quiz grades are shown below.
88, 92, 92, 96, 98
Gabriella scored a 20 on her sixth quiz. What effect does this score have?

• The low score causes the median to increase.

• The low score causes the median to decrease.

• The low score causes the mean to increase.

• The low score causes the mean to decrease.

The prices at several different stores for a pair of shoes are shown below.
$78, $79, $81, $82, $83
Two days later, another store has the same shoes on sale for $65. How does the new price affect the data?

• Only the range was affected.

• The median increased, and the range increased.

• The mean increased, and the range increased.

• The mean decreased and the range increased.

Given the following distributions, which is symmetric?

• Red

• Purple

• Black