Find the mean deviation about the median for the data in Exercises.

Question

Philoid · Accepted Answer

The given observations are already in ascending order. We make a table for the given data, as shown below, adding other columns after calculations.

Now, N = 30 which is even.

Median is the mean of 15^th and 16^th observations. We see that both the 15^th as well as the 16^th observations lie in the cumulative frequency 21, whose corresponding observation is 30.

Therefore, Median

So, we can calculate the absolute values of the deviations from the median, i.e., |x_i – M|, as shown in the table.

Thus, we have

And

Hence, the mean deviation about the median for the given data is 5.1.