3. LEARNING OBJECTIVES
• The aim of the chapter is to make students to
understand Measures of Skewness, Karl Pearson
Co-efficient of Skewness and Bowley's Co-efficient
of skewness
4. LEARNING OUTCOMES
• After this Unit The Students can be able to apply to
Sample Population Data by Differentiating Normal
and Abnormal Distributions with regard to
Dispersion & Skewness.
5. SESSION - 53
• Karl Pearson's Co-efficient of Skewness Under
Continuous Series Problems---------02
6. Karl Pearson's Co-efficient of Skewness
Karl Pearson’s Coefficient of Skewness This method is
most frequently used for measuring skewness. The
formula for measuring coefficient of skewness is given by
SK= Mean - Mode/ S.D
Karl Pearson's Co-efficient of Skewness under
continuous series
Ex ; 1. Compute Karl Pearson's Co-efficient of Skewness
9. CONTD
Modal class = size of highest frequency=25
Assumed Mean = 05, N= 70, fd =117, f d2=341,
C=10, f1=25,f2=12,f0=15,L=10
SK= 𝑋 - Z /𝜎
10. CONTD
Compute Karl Pearson's Co-efficient of Skewness
Calculation of Karl Pearson’s Co-efficient of Skewness
C . I 10 - 20 20 - 30 30 – 40 40 - 50 50 - 60 60 -70
Frequency 15 18 20 12 10 09
C . I F Mid value D= M – A/C Fd Fd2
10 -20 15 15 00 00 00
20 - 30 18 25 01 18 18
30 – 40 20 35 02 40 80
40 - 50 12 45 03 36 108
50 – 60 10 55 04 40 160
60 - 70 09 65 05 45 225
N=84 A = 15 fd=179 f d2=
591
11. CONTD
By inspection method, mode lies in 30 – 40 (Highest
frequency is 20 and corresponding C.I. becomes modal
class) L = 30, f1= 20,f2=12,fo=18,C=10, N=84,A = 15
fd=179, f d2= 591
𝑋 = 15 + 179/ 84 x 10, 𝑋= 5+21.3, 𝑿=36.31
𝜎 = (
591
84
) − (
179
84
)2 x 10, 𝝈 = 15.8
𝜎 = 20 – 18
x 10 Z = 32
Z = 30 + 2(20) – 18 – 12
SK= 𝑋 - Z /𝜎 , SK = 36.31 – 32 / 15.8 , SK = 0.27
12. SUMMARY
As we already discussed and learnt today on skewness
as below
Karl Pearson's Co-efficient of Skewness Under
Continuous Series Problems---------02
13. MCQs
1 . The distribution in which mean = 50 and mode = 60,
will be ____________
a) Symmetrical
b) Positive skewed
c) Negative skewed
d) None of these
2. formula of Karl Pearson co efficient of skewness
a) Sk=mean – mode/ s.d
b) Negatively skewed
c) Symmetrical
d) None of these
14. MCQs
3 . If mean = 36.31 and Mode = 32 and S.D =15.8 then
Karl Pearson co efficient of skewness is
a) 0.27
b) Different
c) Zero
d) None of these
4. If mean = 36.31 and Mode = 32 and Karl Pearson co
efficient of skewness is 0 .27, S.D =?
a) Positive Skewed
b) Negative Skewed
c) 15.8
d) None of these
15. MCQs
5 . The values of mean, median and mode can be
a) Some time equal
b) Never equal
c) Always equal
d) None of these
17. REFERENCES
• S.P. Gupta, Sultan Chand and Sons Publications, 2017
• S. C. Gupta, Himalaya Publishing House,
Fundamentals of Statistics, 2018
• R.S.N Pillai and Bagavathi, S.Chand publications, 2010
