Introduction:
In statistics, the median and the mean are two measures of central tendency used to describe a data set. The median represents the middle value of a data set when it is arranged in ascending or descending order, while the mean is the average of all the values in the data set. For a moderately skewed distribution, the median is twice the mean. This relationship can be explained by understanding the concept of skewness and how it affects the values of the median and the mean.

Skewness:
Skewness is a measure of the asymmetry of a probability distribution. It indicates whether the data is skewed to the left or to the right. A moderately skewed distribution is one where the tail is longer on one side compared to the other, but the skewness is not extreme. In this case, the skewness coefficient is positive or negative but relatively small in magnitude.

Median:
The median is defined as the middle value of a data set. When the data is arranged in ascending or descending order, the median is the value that divides the data into two equal halves. For a moderately skewed distribution, the median tends to be closer to the skewed tail. It is less affected by extreme values, which makes it a robust measure of central tendency.

Mean:
The mean is calculated by summing all the values in a data set and dividing it by the total number of values. It represents the average value of the data set. However, the mean is sensitive to extreme values and can be heavily influenced by outliers. In a moderately skewed distribution, the mean is pulled towards the tail of the distribution, away from the median.

Relationship between the Median and the Mean:
In a moderately skewed distribution, the median is twice the mean. This relationship occurs because the mean is pulled towards the tail of the distribution, making it smaller compared to the median. The skewness causes the mean to be lower than the median, and the magnitude of this difference is approximately twice the value of the mean.

Illustration:
To illustrate this relationship, consider a data set with values {1, 2, 3, 4, 5, 6, 7, 8, 9}. The median of this data set is 5, which is the middle value. The mean is calculated as (1+2+3+4+5+6+7+8+9)/9 = 5. The median is equal to the mean in this case.

Now, let's introduce a moderately skewed distribution by adding an outlier to the data set: {1, 2, 3, 4, 5, 6, 7, 8, 100}. The median remains at 5, as it is not affected by outliers. However, the mean is now calculated as (1+2+3+4+5+6+7+8+100)/9 = 14. The median is approximately twice the mean in this case.

Conclusion:
In a moderately skewed distribution, the median is twice the mean. This relationship occurs because the mean is influenced by extreme values, which pulls it towards the tail of the distribution. The median, on the other hand, is a robust measure of central tendency that is less affected by extreme values. This results in the median being closer to the center of the distribution compared to