The measures of variability refer to the spread or variation of the values around the mean. They are also called measures of dispersion that indicate the degree of diversity in a data set. They also indicate difference within the group. Two different data sets can have the same mean, median or mode but completely different levels of dispersion, or vice versa. Common measures of dispersion or variability are Range and Standard Deviation.
(A) Range
It is the difference between maximum and minimum values of the data (the largest value minus the smallest value). Range can be calculated only for numerical data. It is a measure of dispersion and tells about coverage/spread of data values. For example difference in salaries of employees, marks of a student, price of toys, etc. As range is calculated based on the two extreme values, any outlier in the data badly influences the result. Let M be the largest or maximum value and S is the smallest or minimum value in the data, then Range is the difference between two extreme values i.e. M – S or Maximum – Minimum.
(B) Standard deviation
Standard deviation refers to differences within the group or set of data of a variable. Like Range, it also measures the spread of data. However, unlike Range which only uses two extreme values in the data, calculation of standard deviation considers all the given data. It is calculated as the positive square root of the average of squared difference of each value from the mean value of data. Smaller value of standard deviation means data are less spread while a larger value of standard deviation means data are more spread.
Given n values x1, x2, x3,...xn, and their mean x, the standard deviation, represented as σ (greek letter sigma) is computed as
