MEASURES OF DISPERSION | RANGE

RANGE

Range is the simplest measure of dispersion and is based on position of certain items in a distribution. It is defined as the difference between the two extreme values of a series i.e., the highest value and the smallest value of an item of a distribution in an ascending order.

Range = xn – x1

Xn = last item

X1 = first item

In simple words, Range is the difference between the lowest and the highest values

e.g.: 4, 6, 9, 3, 7

the lowest value is 3

the highest value is 9

thus Range = 9 – 3 = 6

However, it can be misleading,

e.g.: 8, 12, 5, 9, 7, 6, 2616

the lowest value is 5

the highest value is 2616

thus range = 2616 – 5 = 2611

 

In the case of grouped or continuous frequency distribution, range is defined as the difference between the upper limit of the highest class and the lower limit of the smallest class.

If the distributions are in different units, the above definition will be unsuitable. In this case, a relative measure range, coefficient of range can be used.

 

Coefficient of range = Highest value – lowest value

                                       Highest value + lowest value

                                    = xn-x1

                                       Xn+x1

 

Range is easy to calculate and gives an idea about the variability very quickly. But it is greatly affected by fluctuations of sampling as its value varies from sample to sample. It is not suitable for mathematical treatments and is not considered as an appropriate measure in research studies.