Question

in distributions that are skewed to the right, what is the relationship of the mean, median, and mode?

a. mean > median > mode
b. median > mean > mode
c. mode > mean > median
d. mode > median > mean

Explanation:

⚡ Using what you learned: Describing Distributions

Step 1: Understand Right-Skewed Distributions

A right-skewed (or positively skewed) distribution has a long tail stretching toward the larger values on the right side.

Step 2: Compare Measures of Center

• Mode: The peak of the distribution, representing the most frequent value, remains on the left where the bulk of the data is concentrated.
• Median: The middle value of the data set. It is pulled slightly to the right by the larger values in the tail, but is less affected than the mean.
• Mean: The arithmetic average. It is highly sensitive to extreme values and is pulled furthest to the right by the long tail of high values.

Therefore, the relationship is:

$$ \text{mean} > \text{median} > \text{mode} $$

Answer:

A. mean > median > mode