Question

98, 89, 82, 79, 95, 74, 32, 82, 85, 92

what effect does the score of 32 have on the data?

• it has little to no effect on both the mean and the median.
• it has little to no effect on the median, but it makes the mean a less useful measure of center.
• it makes both the mean and the median less useful measures of center.
• it has little to no effect on the mean, but it makes the median a less useful measure of center.

Explanation:

Identify the outlier in the dataset

Using the Outliers knowledge point
The dataset is: \(98, 89, 82, 79, 95, 74, 32, 82, 85, 92\).
The value \(32\) is significantly lower than the rest of the values (which all lie between \(74\) and \(98\)), making \(32\) an outlier.

Analyze the effect on the mean and median

Using the Measures of Center and Robust Statistics knowledge points

• The median is robust to outliers, meaning the inclusion of \(32\) has little to no effect on the median.
• The mean is highly sensitive to outliers; the extremely low value of \(32\) pulls the mean down, making it unrepresentative of the bulk of the data and thus a less useful measure of center.

Match with the correct option

Using the Robust Statistics knowledge point

• The statement "It has little to no effect on the median, but it makes the mean a less useful measure of center" correctly describes this behavior.

Answer:

• It has little to no effect on both the mean and the median.
• It has little to no effect on the median, but it makes the mean a less useful measure of center. (Correct answer)
• It makes both the mean and the median less useful measures of center.
• It has little to no effect on the mean, but it makes the median a less useful measure of center.