Find the standard deviation, s, of sample data summarized in the frequency distr

Question

Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. s = Squareroot n[sigma (f + x^2)] - [sigma (f + x)]^2/n(n - 1) Standard deviation = (Round to one decimal place as needed.)

Explanation / Answer

The values of x and f will be:

The statistical software output for standard deviation of above table is:

Approximate summary statistics:
Using counts in Frequency (f)

Hence,

Standard deviation = 9.5

Class Midpoint (x) Frequency (f) 30 - 36 33 2 37 - 43 40 1 44 - 50 47 5 51 - 57 54 2 58 - 64 61 17 65 - 71 68 30 72 - 78 75 37

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