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,

11.111.1.

sequals=StartRoot StartFraction n left bracket Summation from nothing to nothing left parenthesis f times x squared right parenthesis right bracket minus left bracket Summation from nothing to nothing left parenthesis f times x right parenthesis right bracket squared Over n left parenthesis n minus 1 right parenthesis EndFraction EndRootnf•x2(f•x)2n(n1)

Interval

3030-3636

3737-4343

4444-5050

5151-5757

5858-6464

6565-7171

7272-7878

Frequency

22

33

88

11

88

3636

3333

Standard

deviationequals= (ANSWER!)

(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?

Interval

3030-3636

3737-4343

4444-5050

5151-5757

5858-6464

6565-7171

7272-7878

Frequency

22

33

88

11

88

3636

3333

Explanation / Answer

Here the mid point of interval and the require values.

Here variance =  f•x2(f•x)2/n) / [n(n1)] = (223798 - 35522/58)/ ( 57) = 109.9758

Standard deviation = sqrt (109.9758) = 10.487

Here the computed values is similar to the given standard deviation 11.1.

Interval Midpoint Frequency f.x f.x^2 30-36 33 2 66 2178 37-43 40 3 120 4800 44-50 47 8 376 17672 51-57 54 1 54 2916 58-64 61 8 488 29768 65-71 68 36 2448 166464 Sum 58 3552 223798

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