CBSE Class 11-science Answered

$T h e space f o l l o w i n g space g i v e s space t h e space f r e q u e n c y space d i s t r i b u t i o n space o f space t h e space d a i l y space c o m m u t i n g space t i m e left parenthesis i n space m i n right parenthesis f r o m space h o m e space t o space w o r k space f o r space a l l space 25 space e m p l o y e e s space o f space a space c o m p a n y colon$ 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 | 16 Nov, 2016, 06:06: AM

Expert Answer

Daily commuting time	Frequency f_i	x_i	f_ix_i	f_ix_i²
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

$M e a n equals fraction numerator begin display style sum for i of end style f subscript i x subscript i over denominator begin display style sum for i of end style f subscript i end fraction equals fraction numerator 20 plus 135 plus 150 plus 140 plus 90 over denominator 4 plus 9 plus 6 plus 4 plus 2 end fraction equals 535 over 25 equals 21.40 V a r i a n c e equals fraction numerator begin display style sum for i of f subscript i x squared subscript i end style over denominator begin display style sum for i of f subscript i end style end fraction minus m e a n squared equals fraction numerator 100 plus 2025 plus 3750 plus 4900 plus 4050 over denominator 25 end fraction minus 457.96 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 14825 over 25 minus 457.96 equals 135.04 S tan d a r d space d e v i a t i o n equals square root of V a r i a n c e end root equals 11.62$