Mean deviation about median is a measure of dispersion that quantifies how much the values in a distribution deviate from the median. It is calculated by taking the absolute value of the difference between each observation and the median, summing these values, and dividing by the total number of observations.

Here's how to calculate the mean deviation about median for the given distribution:

Step 1: Find the median
To find the median, we need to arrange the observations in ascending order. The middle value is the median. If there are an even number of observations, the median is the average of the two middle values.

X: 3 5 7 9 11 13 15
F: 2 8 9 16 14 7 4

Arranging in ascending order: 3 5 7 9 11 13 15
Median = 9 (the fourth observation)

Step 2: Calculate the deviation from the median for each observation
We need to find how much each observation deviates from the median. We do this by subtracting the median from each observation and taking the absolute value.

Deviation from the median (|X - median|):
2 |3 - 9| = 6
8 |5 - 9| = 4
9 |7 - 9| = 2
16 |9 - 9| = 0
14 |11 - 9| = 2
7 |13 - 9| = 4
4 |15 - 9| = 6

Step 3: Calculate the mean deviation about median
We need to find the average deviation from the median by adding up all the deviations from the median and dividing by the total number of observations.

Mean deviation about median = (6 + 4 + 2 + 0 + 2 + 4 + 6) / 50 = 24/50 = 0.48

Therefore, the mean deviation about median for the given distribution is 0.48.

Note: The mean deviation about median is a measure of dispersion that is less affected by extreme values than the standard deviation. It is useful when the distribution is skewed or has outliers.