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

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

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 EndRootn?f•x2??(f•x)2n(n?1)

Interval

20?-29

303-39

40?-49

505-59

60?-69

70?-79

80?-89

Frequency

1

1

8

1

13

29

35

Interval

20?-29

303-39

40?-49

505-59

60?-69

70?-79

80?-89

Frequency

1

1

8

1

13

29

35

Explanation / Answer

Here the frequency table is

Variance = [?f•x2??(f•x)2/n] [1/(n?1)] = (235643.3 - 3468.52/53) * (1 /52)

= 166.4006

Standard deviation = sqrt(166.4006) = 12.90

Interval Frequency(f) Midpoint(x) fx fx^2 20-29 1 24.5 24.5 600.25 30-39 1 34.5 34.5 1190.25 40-49 8 44.5 356 15842 50-59 1 54.5 54.5 2970.25 60-69 13 64.5 838.5 54083.25 70-79 29 74.5 2160.5 160957.3 Sum 53 3468.5 235643.3

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