MEASURES OF DISPERSION OF UNGROUPED DATAMean Deviation (average absolute deviation)The formula for mean deviation is shown below.

Example

Mean deviation is not used for higher statistical work. The useful measures of dispersion are variance and standard deviation.Population variance and Standard deviation of ungrouped dataVariance determines how the values fluctuate around the mean. The population variance is the mean value of the square of the deviation from the mean as is denoted by the symbol sigma square. The formula is shown below.

Another form of the formula which is more convenient to use is as follows:

Standard deviation is the square root of the varianceOne form of the formula is as shown below.

ExampleFind the variance and standard deviation of the following data.XFrequency, f

12

38

410

68

106

Solution

Sample variance and Standard deviation of ungrouped dataThe sample variance for a sample of n measurements is the sum of the squared distance of the measurements from the mean divided by (n-1) and it is denoted by the symbol s2. Several forms of the formula are shown below.

Formula for sample standard deviation is as shown below.

ExampleFind the variance and standard deviation of the following sample data: 1, 7, 2 and 5.Solution

= 12 +72 +22 + 52 = 79