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 given 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, 9.0. s = Squareroot n[sigma (f - x^2)] - [sigma (f - x)]^2/n(n - 1) Standard deviation = (Round to one decimal place as needed.) Consider a difference of 20% between two values of a standard deviation to be significant. How does this computed value compare with the given standard deviation, 9.0? A. The computed value is significantly greater than the given value. B. The computed value is significantly less than the given value. C. The computed value is not significantly different from the given value.

Explanation / Answer

The table is as given below

Sum(f * X2) = 207631.8, Sum (f * X)2 = 4185891 and n = 87

Putting these values in the given equation for s = SQRT{[ (n(Sum(f * X2) - Sum (f * X)2] / (n(n-1) }

s = SQRT {[ (87 * 207631.8) - 4185891] / [87(87-1)]} = 43.1

Comparing with a standard deviation of 9, the the % difference = (43.1-9)/9 = 379% more than the given value.

Therefore OPTION A is the correct answer

Class x=mid pt Frequency x2 f*x2 f*x (f*x)2 20-29 24.5 5 600.25 3001.25 122.5 15006.25 30-39 34.5 15 1190.25 17853.75 517.5 267806.3 40-49 44.5 35 1980.25 69308.75 1557.5 2425806 50-59 54.5 19 2970.25 56434.75 1035.5 1072260 60-69 64.5 8 4160.25 33282 516 266256 70-79 74.5 5 5550.25 27751.25 372.5 138756.3 Total 87 207631.8 4185891

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