Question

define and distinguish among mean, median, and mode

choose the correct description of the mean below.

a. the mean is the sum of all the values divided by the number of values. it is not affected by outliers

b. the mean is the most common value in a data set. it can be strongly affected by outliers

c. the mean is the most common value in a data set. it is not affected by outliers

d. the mean is the sum of all the values divided by the number of values. it can be strongly affected by outliers

e. the mean is the middle value in a data set. it can be strongly affected by outliers

f. the mean is the middle value in a data set. it is not affected by outliers

Explanation:

To determine the correct description of the mean:

• Recall the definition of the mean: it is calculated as the sum of all values divided by the number of values (formula: $\text{Mean} = \frac{\sum x}{n}$).
• Analyze the effect of outliers: Since the mean uses all values in its calculation, a very large or small outlier can pull the mean towards it, so the mean is strongly affected by outliers.
• Now evaluate the options:
• Option A: Claims the mean is not affected by outliers, which is incorrect.
• Option B: Describes the mode (most common value), not the mean.
• Option C: Describes the mode and claims no outlier effect, incorrect.
• Option D: Correctly defines the mean as sum of values over number of values and notes it is strongly affected by outliers.
• Option E: Describes the median (middle value), not the mean.
• Option F: Describes the median and claims no outlier effect, incorrect.

Answer:

D. The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers