Measures of dispersion(BASICS)

Measures of dispersion are those used to show the degree of variation of the data from its central value.

These measures are of importance because it is used to test the reliability of an average, to be certain of any existence of a high variation in the data, to estimate trends and also for comparison purposes.

There are 4 measures of dispersion :
1. Range
2. Mean Deviation
3. Quartile Deviation
4. Standard Deviation



Range is the difference between the largest value and the smallest value in the data.
It is denoted by R.

R = L-S
where L is the largest variable and S is the smallest.
coefficient of R = (L-S) / (L+S)

Mean Deviation is the value computed by taking the arithmetic mean of the absolute values of the deviations of the functional values from some central value of the data(the mean or the median or the mode).It is denoted by MD.

where; N is the total frequency, f is the frequency and m is the mid value.
coefficient of 
1.MD from mean = MD / x̅ 
2.MD from median = MD / M
3.MD from mode = MD / Z

Quartile Deviation is half of the difference between the third and the first quartile.
It is also known as the semi quartile range. It is denoted by QD.

QD = [(Q3) - (Q1)] / 2
where Q3 is the third quartile and Q1 is the first.
coefficient of QD = [(Q3) - (Q1)] / [(Q3) + (Q1)]  

Standard Deviation is again a measure of dispersion.It is the value computed by obtaining the square root of variance by determining the variation between each data point relative to the mean. It is denoted by SD or σ.

coefficient of σ = σ / x̅
coefficient of variance = σ / x̅ * 100.

The standard deviation is the square root of the variance.