Mean Deviation about Mode
The term with the highest frequency in the data set is the mode of the data set. The formula to calculate the mean deviation of the data set about the mode is,
For Ungrouped Data,
Mean Deviation = ∑in (xi – M) / n
Where M represents the mode of the data set.
For Discrete Frequency Distribution,
Mean Deviation = ∑in fi(xi – M) / ∑in fi
Where M represents the mode of the data set.
For Continuous Frequency Distribution,
Mean Deviation = ∑in fi(xi – M) / ∑in fi
where,
M represents the mode of the data set and is calculated as,Mode = l + [(f – f1) / (2f – f1 – f2)] × h
Where,
- l is the lower value of the modal class,
- h is the size of the modal class,
- f is the frequency of the modal class,
- f1 is the frequency of the class preceding the modal class, and
- f2 is the frequency of the class succeeding the modal 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.