MEASURES OF DISPERSION IN STATISTICS
MEAN DEVIATION
Average deviation or mean deviation is the average difference between the items in a series from the mean or median or mode of that series. Theoretically, it is beneficial to take deviations from median, because the sum of deviations of items from Median, is minimum when plus and minus signs are ignored. But, often mean is used for its calculation, so it is called mean deviation. The mean deviation is also called as the first moment of dispersion.
ACCORDING TO CLARK AND SCHKADE
“Average deviation is the average amount of scatter of the items in a distribution from either the mean or the median, ignoring the signs of the deviations. The average that is taken of the scatter is an arithmetic mean, which accounts for the fact that this measure is often called the mean deviation.”
The formula for calculating mean deviation is
| FORMULAE OF MEAN DEVIATION | |
| Individual series | MD= Σ | d |/N |
| Discrete series | MD= Σ f| d |/N |
| Continuous Series | MD= Σ f| d |/N |
MERITS OF MEAN DEVIATION:
1 It is relatively simple to calculate and easy to understand. It is very close to arithmetic mean. In order to give information to persons having no knowledge of statistics the measure of mean deviation is more useful.
2. It is based on all the items of the series. Any small change in the series would affect the values of mean deviation.
3. It is less affected by the extreme items as compared to standard deviation.
4. Mean deviation is useful for comparison because the deviations are taken from actual mean or median or mode.
5. It is based on measurement rather than estimation.
6. It is widely used in economics, socio-economic field and business.
7. Mean deviation is rigidly defined like that of an ideal measure of dispersion.
8. As mean deviation is based on the deviation about an average, it provides us a better measure for comparison.
9. It gives us accurate results. The averaging of the absolute deviation from an average removes the irregularities in the distributions.
DEMERITS OF MEAN DEVIATION
- In mean deviation plus minus signs are ignored, which is not justified mathematically. This limitation makes mean deviation useless for further mathematical treatment.
- The mean deviation calculated from mode is not reliable, because mode in many cases is indeterminate. Even the mean deviation calculated from median is not reliable If we use arithmetic mean, then it loses scientific character because the sum of deviations from mean is greater than the sum of deviations from median when plus minus signs are ignored.
- If mean, median and mode are in fractions, then the calculation of mean deviation becomes cumbersome
- It is generally not useful for statistical inferences as it is not a satisfactory measure when taken from mode or dealing with a skewed distribution. Theoretically, mean deviation gives us the best results when deviations are taken from Median. But median is not a satisfactory measure when the distribution has large variations.
- From mean deviations of different groups of series, it is not possible to find out the combined mean deviation of all groups taken together. It means, mean deviation is not capable of further algebraic treatment.
- It is rarely used for sociological studies.
- In case of open-end classes mean deviation cannot be calculated. 8. It has a tendency to increase with the sample size though not in the same ratio.
- statistical techniques. It is useful for small samples also where no detailed analysis is required.