Mean Deviation about Median
The middle point of the data set when arranged in ascending or descending order is called the median of the data set. it is the middle value of the data set which divides the data set into two equal halves. The formula to calculate the mean deviation of the data set about the mean is,
For Ungrouped Data,
Mean Deviation = ∑in (xi – M) / n
Where M represents the middle point or median of the data set and is calculated as,
- For n = odd terms,
- M = [(n + 1)/2]th observation
- For n = even terms,
- M = [(n/2)th + (n/2 + 1)th] / 2
For Discrete Frequency Distribution,
Mean Deviation = ∑in fi(xi – M) / ∑in fi
Where M represents the middle point or median of the data set and is calculated in the same way as above.
For Continuous Frequency Distribution,
Mean Deviation = ∑in fi(xi – M) / ∑in fi
Where M represents the middle point or median of the data set and is calculated as,
M = l + {[∑in fi/2 – cf] / f}×h
Where,
- cf is the cumulative frequency of the class preceding the median class,
- l is the lower value of the median class,
- h is the length of the median class, and
- f is the frequency of the median class.
Mean Deviation
We define the mean deviation of the data set as the value which tells us how far each data is from the centre point of the data set. The centre point of the data set can be the Mean, Median or Mode. Thus, the mean of the deviation of all the data in a set from the centre point of the data set is called the mean deviation of the data set. We can calculate the mean deviation for both Grouped data and ungrouped data. Mean deviation measures the arbitrary change in the values of the data set from the centre point of the data set.