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T h e space f o l l o w i n g space g i v e s space t h e space f r e q u e n c y space d i s t r i b u t i o n space o f space t h e space d a i l y space c o m m u t i n g space t i m e left parenthesis i n space m i n right parenthesis
f r o m space h o m e space t o space w o r k space f o r space a l l space 25 space e m p l o y e e s space o f space a space c o m p a n y colon

Daily commuting time

No of people

0-10

4

10-20

9

20-30

6

30-40

4

40-50

2

C a l c u l a t e space t h e space m e a n space v a r i a n c e space a n d space s tan d a r d space d e v i a t i o n

Asked by Topperlearning User 16th November 2016, 6:06 AM
Answered by Expert
Answer:

Daily commuting time

Frequency fi

xi

fixi

fixi2

0-10

4

5

20

100

10-20

9

15

135

2025

20-30

6

25

150

3750

30-40

4

35

140

4900

40-50

2

45

90

4050

M e a n equals fraction numerator begin display style sum for i of end style f subscript i x subscript i over denominator begin display style sum for i of end style f subscript i end fraction equals fraction numerator 20 plus 135 plus 150 plus 140 plus 90 over denominator 4 plus 9 plus 6 plus 4 plus 2 end fraction equals 535 over 25 equals 21.40
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 begin display style sum for i of f subscript i end style end fraction minus m e a n squared equals fraction numerator 100 plus 2025 plus 3750 plus 4900 plus 4050 over denominator 25 end fraction minus 457.96
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 space space space space equals 14825 over 25 minus 457.96 equals 135.04
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 11.62

Answered by Expert 16th November 2016, 8:06 AM
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