Mean deviation about mean is a measure of the dispersion or spread of a data set. It calculates the average deviation of each data point from the mean of the data set.

To calculate the mean deviation about mean, follow these steps:

1. Calculate the mean of the data set.
2. Find the absolute difference between each data point and the mean.
3. Sum up all the absolute differences.
4. Divide the sum by the number of data points.

Now, let's calculate the mean deviation about mean for the given data set: 50, 60, 50.

Step 1: Calculate the mean of the data set.
Mean = (50 + 60 + 50) / 3
Mean = 160 / 3
Mean = 53.33

Step 2: Find the absolute difference between each data point and the mean.
Absolute differences: |50 - 53.33|, |60 - 53.33|, |50 - 53.33|
Absolute differences: 3.33, 6.67, 3.33

Step 3: Sum up all the absolute differences.
Sum of absolute differences = 3.33 + 6.67 + 3.33
Sum of absolute differences = 13.33

Step 4: Divide the sum by the number of data points.
Mean deviation about mean = Sum of absolute differences / Number of data points
Mean deviation about mean = 13.33 / 3
Mean deviation about mean = 4.44

Therefore, the mean deviation about mean for the given data set is 4.44.

Explanation:

The mean deviation about mean represents the average deviation of each data point from the mean value. It is a measure of the spread or dispersion of the data set.

In this case, the mean of the data set is calculated to be 53.33. Then, the absolute difference between each data point and the mean is calculated. These absolute differences are 3.33, 6.67, and 3.33.

The sum of these absolute differences is 13.33. Finally, the mean deviation about mean is obtained by dividing the sum of absolute differences by the number of data points, which is 3 in this case. The mean deviation about mean for the given data set is calculated to be 4.44.

The mean deviation about mean provides an indication of how closely the data points are clustered around the mean. A smaller mean deviation about mean indicates that the data points are closely clustered around the mean, while a larger mean deviation about mean indicates a greater dispersion or spread of the data points.