Math, asked by rrajesshwarik, 1 month ago

Calculate Karl Pearson's coefficient of skewness from the following data. Marks scored 0-20 20-40 40-60 60-80 80-100 No of students 8 12 30 10 20 ng table​

Answers

Answered by amitnrw
1

Given :  

Marks scored    0-20 20-40 40-60 60-80 80-100

No of students   8          12       30       10       20

To Find : Karl Pearson's coefficient of skewness

Solution:  

Karl Pearson's coefficient of skewness = (mean - Mode)/SD

= 3 ( Mean - Median ) / SD

Marks scored  CM x   No of students  f         xf                 cf

0-20                  10        8                                80                8

20-40                30       12                              360              20

40-60               50        30                            1500             50

60-80              70         10                             700              60

80-100             90        20                             1800            80

                                     80                            4440

Mean = 4440/80  =  55.5

80/2 = 40

Median = 40  + 20 * ( 40 - 20)/30  

= 40 + 40/3

= 53.33

Mode =  40  + 20 *  (30 - 12)/(30 - 12 + 30 - 10)

= 40 + 360/38

= 49.47

SD =  √∑fi(xi - Mean)² / n    =   √  51180/80  = 25.29

 

Karl Pearson's coefficient of skewness = (mean - Mode)/SD

=  (55.5 - 49.47)/25.29

= 0.2384

Karl Pearson's coefficient of skewness =

 3 ( Mean - Median ) / SD

= 3 (55.5  - 53.33)/25.29

= 0.2574

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