To find the mean deviation about the median, we have to find the median of the given discrete frequency distribution. Now, we have to find the sum of the frequencies (Σfi = N) and cumulative frequencies, after arranging the observations in either ascending or descending order. Then we identify the observation whose cumulative frequency is equal to or just greater than N/2. This is called the median of the data. Now we can find the mean deviation about median with the formula,
M.D = , where M = median.
b) Continuous frequency distribution:
Recall that a continuous frequency distribution is a series in which the data is classified into different class-intervals (without page) along with their respective frequency (fi).
i) Mean deviation about mean for grouped data
Recall that while computing the arithmetic mean of a continuous frequency distribution, we assumed that the entire frequency fi of the i-th class interval is centred at the midpoint xi of that class interval. In the discussion that follows, we adopt in much the same procedure and write the midpoint (xi) of each class interval. With these xi, we proceed to find the mean deviation, as has been done in the case of a discrete frequency distribution.
Alternative method to find M.D about mean (Step-deviation method):
We can avoid tedious calculations of computing the mean x by following step deviation method. In this method we take an assumed mean which is the middle or just close to it in the data. Then deviation of the observations or midpoints of classes are taken from the assumed mean. Now the mean can be calculated by the formula
x = A + × C
where A = assumed mean, di =
i.e, x = A + Cd, where d =