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
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Answers
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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