Dispersion is defined as the extent to which values differ from their average. Mean deviation of a series is the arithmetic mean of the absolute deviation of various items taken from central values i.e. Mean, Median or Mode. Mean Deviations are absolute, which implies positive (+ve) and negative (–ve) signs are ignored while calculating Mean deviation.
The measures of mean deviation can be classified as absolute measure which includes mean deviation form mean and median and relative measure which includes the coefficient of mean deviation form mean and median. Mean Deviation can be calculated in three types of series individual series, discrete series and continuous series. For individual and discrete series, the mean deviation from mean can be calculated from actual mean or direct method and for continuous series it can be calculated by the actual mean or direct as well as assumed mean or indirect method. The mean deviation from median can be calculated for all the three series by the direct method. The coefficient of mean deviation can be calculated by dividing the mean deviation from mean by the mean or by dividing the mean deviation from median by the median. Like other measures of dispersion, mean deviation has many merits and demerits.
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Dispersion of the series is expressed in terms of some relative value inMarks:1
relative measure of dispersion.
Since relative measures are free from the units in which the values have been expressed, they can be compared even across different groups having different units of measurement.
One of the merits of mean deviation isMarks:1
based on all the items.
The followings are the merits of mean deviations:
- It is based on all the items.
- It is rigidly defined and its value is precise and definite.
- It is simple to calculate and understand
If Median = 25 and MDmedian = 9, then coefficient of mean deviation about median isMarks:1
Coefficient of mean deviation about median = MDmedian / Median = 9 / 25 = 0.36
If Mean = 15.6 and MDmean = 4.2, coefficient of mean deviation about mean isMarks:1
Coefficient of mean deviation about mean = MDmean / Mean = 4.2 / 15.6 = 0.27
The given below formula is ofMarks:1
Mean deviation of a series is the arithmetic mean of the absolute deviations of various items taken from central values i.e. Mean, Median or Mode.