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.
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.
