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------------------------------------------------ If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?

A. 122
B. 130
C. 126
D. 118

Answer :

Certainly! Let's go through the problem step-by-step to determine which value could be the median of a positively skewed distribution where the mean is 122.

1. Understand the Shape of a Positively Skewed Distribution:
- In a positively skewed (right-skewed) distribution, the tail on the right side of the distribution is longer or fatter than the left side.
- This causes the mean to be greater than the median because the mean is affected more by the extreme higher values.

2. Relationship Between Mean and Median:
- Since the distribution is positively skewed, typically, the mean is greater than the median.

3. Given Information:
- The mean of the distribution is 122.
- We are given four possible options for the median: 122, 130, 126, and 118.

4. Determine Which Value Could Be the Median:
- The value of the median should be less than the mean in a positively skewed distribution.
- From the options provided, the value that is less than 122 is 118.

5. Conclusion:
- Therefore, the value that could be the median of this positively skewed distribution is 118.

This step-by-step approach helps us identify 118 as a reasonable estimate for the median in a positively skewed distribution where the mean is 122.