Mean Deviation about Median

The mean deviation about median is a measure of dispersion that shows the average distance between each data point and the median of the data set. It is calculated by finding the absolute difference between each data point and the median, then taking the average of these differences.

Calculating the Median

To calculate the median of the data set X 3,5,7,9,11,13,15, we first need to arrange the data set in order from smallest to largest:

3, 5, 7, 9, 11, 13, 15

The median is the middle value in the data set. Since there are 7 values in this data set, the median is the fourth value:

3, 5, 7, 9, 11, 13, 15

So the median is 9.

Calculating the Mean Deviation about Median

Next, we need to find the absolute difference between each data point and the median:

|3-9| = 6
|5-9| = 4
|7-9| = 2
|9-9| = 0
|11-9| = 2
|13-9| = 4
|15-9| = 6

Then, we need to find the average of these absolute differences, which is the mean deviation about median:

(6 + 4 + 2 + 0 + 2 + 4 + 6) / 7 = 24 / 7 ≈ 3.43

So the mean deviation about median for the data set X 3,5,7,9,11,13,15 is approximately 3.43.

Conclusion

In summary, the mean deviation about median is a measure of dispersion that shows the average distance between each data point and the median of the data set. It is calculated by finding the absolute difference between each data point and the median, then taking the average of these differences. In the case of the data set X 3,5,7,9,11,13,15, the median is 9 and the mean deviation about median is approximately 3.43.

3.4285