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The population and the sample variance of grouped data are computed by using the following formulas:

(2.6.4)

(2.6.5)

where and are as defined earlier in this section.

Example 2.6.3 (Variance of a grouped data) Determine the variance of the grouped data in Example 2.6.1.

Solution: From the data in Table 2.1, we have

Substituting these values and in formula (2.6.5), we obtain

The population and the sample standard deviation are found by taking the square root of the corresponding variances. For example, the standard deviation for the grouped data in Example 2.6.1 is