Question

1. which of the following statements about the mean and median is true?

○ a. the mean is influenced by extreme values more than the median.
○ b. the mean is the middle value in a dataset.
○ c. the mean and median are always equal.
○ d. the median is always a whole number.

Explanation:

• Option a: The mean is calculated as the sum of all values divided by the number of values. Extreme values (outliers) can significantly pull the mean up or down. The median is the middle value when data is ordered, so it is less affected by extreme values. This statement is correct.
• Option b: The median is the middle value in a dataset (when ordered), not the mean. The mean is the average. So this is incorrect.
• Option c: The mean and median are not always equal. For example, in a skewed dataset (like [1, 2, 100]), the mean (≈34.33) and median (2) are different. So this is incorrect.
• Option d: The median can be a non - whole number. For example, in the dataset [1, 2, 3, 4], the median is $\frac{2 + 3}{2}=2.5$, which is not a whole number. So this is incorrect.

Answer:

a. The mean is influenced by extreme values more than the median.