Find the mean variance and standard deviation for the following data

 Interval (group) Frequency 37-46 19 47-56 23 57-66 27 67-76 28
Please provide solution to this question

Asked by Topperlearning User | 16th Nov, 2016, 06:21: AM

Expert Answer:

Interval

Frequency fi

xi

fixi

fixi2

36.5-46.5

19

41.5

788.5

32722.5

46.5-56.5

23

51.5

1184.5

61001.5

56.5-66.5

27

61.5

1660.5

102120.5

66.5-76.5

28

71.5

2002

143143

m e a n equals fraction numerator begin display style sum for i of end style f subscript i x subscript i over denominator sum for i of f subscript i end fraction equals fraction numerator 788.5 plus 1184.5 plus 1660.5 plus 2002 over denominator 97 end fraction equals 58.09
v a r i a n c e equals fraction numerator begin display style sum for i of f subscript i x squared subscript i end style over denominator sum for i of f subscript i end fraction minus m e a n squared equals fraction numerator 32722.5 plus 61001.5 plus 102120.5 plus 143143 over denominator 97 end fraction minus 3375.37
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 3494.72 minus 3375.37 equals 119.35
s tan d a r d space d e v i a t i o n equals square root of v a r i a n c e end root equals 10.92

Answered by  | 16th Nov, 2016, 08:21: AM

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