Statistics Median vs Mean and Interquartile Range vs Standard Deviation

In the data set shown, how would adding a 200 change the mean and median?

14, 15, 16, 17, 18, 19

• The mean would increase a lot, the median would increase only a little.

• The mean and median would both increase a lot.

• The median would increase a lot, the mean would increase only a little.

• The mean and median would stay the same.

Answer explanation

Adding a really big outlier causes the mean to increase, but it doesn't really affect the median at all.

The table below shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.

The team signs an additional player to a contract worth 10 million dollars per year. Which statement about the median and mean is true?

• Both will increase.

• Only the median will increase.

• Only the mean will increase.

• Neither will change.

Which best represents the Interquartile Range?

• 15

• 85

• 93

• 78

The following boxplot shows the heights of students in Kyra’s Health class. Which measures of center spread should be used to describe it?

• Mean and Standard Deviation because the shape of the data is normal.

• Mean and IQR because the shape of the data is normal.

• Median and Standard Deviation because the shape of the data is skewed.

• Median and IQR because the shape of the data is skewed.

Answer explanation

When data is normal in shape, we use the mean and standard deviation to describe it because there are no really high or really low data value skewing the data in one direction.

Find the measures of variation for the data set.

• 1.4

• Median (Q2)

• 0.5

• Q3

• 8.9

• Q1

• 8.75

• Range

• 9.25

• IQR

Michael has taken 12 tests in his math class. His lowest test score was 78. His highest test score was 98. On the 13th test, he earned a 64. Which of the following effects are certain to occur to the standard deviation, mean, and median of Michael's test scores when the last score is added?

• The standard deviation, median, and mean all decrease.

• The standard deviation increases, mean decreases, and median cannot be determined.

• The standard deviation increases, and mean and median decrease.

• The standard deviation cannot be determined, and mean and median decrease.

Find the measures of variation for the data set.

• 9.25

• IQR

• 0.5

• Range

• 1.4

• Q3

• 8.75

• Q1

• 8.9

• Median (Q2)

If Jennifer scored an 86 on her test, how does she compare to the rest of the students in her class?

• Jennifer scored in the top 25% of her class.

• There is no way of knowing how Jennifer did compared to the rest of her class.

• There were not a lot of students who scored between 85 and 95 because the whisker on the higher end of the data is shorter.

Answer explanation

A box and whisker plot uses the five number summary to split data into four sections, each containing 25% of the data. Since Jennifer scored an 86, that puts her in the top 25%.

The boxplots below show test scores from Mr. Payne’s 1^st and 2^nd period classes.

Which class typically performed better?

• First period

• Second period

Answer explanation

Second period performed better because the data is less spread out, meaning their scores were more consistently higher than first period.

Find the median.
12, 5, 9, 18, 22, 25, 5

• 9

• 8

• 12

• 18