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-l 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, 11-1? A. The computed value is significantly greater than the given value. B. The computed value is not significantly different from the given value. C. The computed value is significantly less than the given value.

Explanation / Answer

Sum of f.x^2 = 592730.5

n*(Sum of f.x^2) = 82*592730.5 = 48603901

Sum of f.x = 6899

(Sum of f.x)^2 = 6899^2 = 47596201

n*(Sum of f.x^2) - (Sum of f.x)^2 = 1007700

[n*(Sum of f.x^2) - (Sum of f.x)^2]/n(n-1) = 1007700/(82*81) = 151.72

So s = sqrt(151.72) = 12.3

So Standard deviation = 12.3

But given standard deviation = 11.1

Difference = 12.3 - 11.1 = 1.2

which is less than 20%

So option B

The computed value is not significantly different from the given value.

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