Question

any decrease in the lowest score in any distribution must result in a change in which of the following?
select one:
a. median only
b. mean only
c. mode only
d. median and mode only
e. mean and median only

Explanation:

• Median: The median is the middle value of an ordered dataset. Decreasing the lowest score does not change the position of the middle value(s), so the median stays the same.
• Mode: The mode is the most frequently occurring value. Lowering the lowest score does not affect the frequency of other values, so the mode remains unchanged.
• Mean: The mean is calculated as $\frac{\text{Sum of all values}}{\text{Number of values}}$. Decreasing the lowest score reduces the total sum, while the number of values stays the same, so the mean must decrease.

Answer:

b. mean only