This document discusses Karl Pearson's Coefficient of Skewness, a method for measuring the skewness of a data distribution. It provides examples of calculating the coefficient under individual and discrete series. For an individual series with data points ranging from 35 to 75 and a mean of 55, the coefficient is calculated to be 0.77, indicating positive skewness. For a discrete series with wage data, the coefficient is calculated to be -0.26, indicating negative skewness. The document also includes multiple choice questions to test understanding of skewness and the relationships between the mean, median and mode of a distribution.

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 52

2. RECAP
• Meaning & Definition of Skewness, Measures of
Skewness

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 - 51
• Karl Pearson's Co-efficient of Skewness Under
Individual and Discrete 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 individual
series
Ex ; 1. Compute Karl Pearson's Co-efficient of Skewness
X; 50,55,45,65,70,45,75,35

7. CONTD
Calculation of Karl Pearson's Co-efficient of Skewness
X X = X - 𝑋 𝑥2
50 -05 = 50-55 25
55 00 = 55-55 00
45 -10 = 45-55 100
65 10 = 65-55 100
70 15 = 70-55 225
45 -10 = 45-55 100
75 20 = 75-55 400
35 -20 = 35-55 400
𝑋 =440 𝑥2 = 1350

8. CONTD
𝑋 = 𝑋/ N S.D = 𝑥2/N
𝑋 = 440/8= 55 S.D= 1350/8,
S.D = 168.75 = 13
MODE= Most repeated value is 45 ( two times) Z = 45
SK = MEAN – MODE/S.D
SK = 55 – 45/13
SK = 10 / 13
SK = 0. 769 or 0.77

9. KPCS under Discrete Series
EX; 02, Compute Karl Pearson's Co-efficient of
Skewness under Discrete series
𝑋 = 𝑓𝑥/ N , S.D = 𝑓 𝑥2/N, Mode is highest
frequency is 25 and Corresponding WAGES or X value
becomes Mode, Z= 30
Calculation Karl Pearson's Co-efficient of Skewness
under Discrete series in Next Slide
Wages 15 20 25 30 35 40 45
No. of
Persons
3 19 16 25 4 6 5

10. CONTD
Wages (X) No of
persons (f)
fx X = X - 𝑿 𝒙𝟐 f𝒙𝟐
15 03 45 -13=15-28 169 0507
20 19 380 -8 =20-28 064 1216
25 16 400 -3 = 25-28 009 0144
30 25 750 2 = 30-28 004 0100
35 04 140 7 = 35-28 049 0196
40 06 240 12 = 40-28 144 0864
45 05 225 17= 45-28 289 1445
N = 78 𝒇𝒙 =2180
𝑋 = 𝑓𝑥/ N
𝑋 = 2180/ 78
𝑿 =27.94 or
28
𝒇 𝒙𝟐=4472
S.D = 𝑓 𝑥2/N
S.D = 4472/7
S.D = 57.33
S.D = 7.57

11. CONTD
𝑋 = 𝑓𝑥/ N , S.D = 𝑓 𝑥2/N, Mode is highest
frequency is 25 and Corresponding WAGES or X value
becomes Mode, Z = 30
𝑋 = 28, S.D = 7.57, Z = 30
SK = MEAN – MODE/S.D
SK = 28 – 30/7.57
SK = - 2/7.57
SK = - 0. 26

12. SUMMARY
As we already discussed and learnt today on skewness
as below
Karl Pearson's Co-efficient of Skewness Under
Individual and Discrete Series Problems----------02

13. MCQs
1 . The distribution in which mean = 60 and mode = 50,
will be ____________
a) Symmetrical
b) Positive skewed
c) Negative skewed
d) None of these
2. If mean is less than mode, the distribution will be
a) Positively skewed
b) Negatively skewed
c) Symmetrical
d) None of these

14. MCQs
3 . In symmetrical distribution, mean, median, and mode
are:
a) Equal
b) Different
c) Zero
d) None of these
4. If mean, median, and mode are all equal then
distribution will be
a) Positive Skewed
b) Negative Skewed
c) Symmetrical
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

16. CONTD
ANSWERS
1. B
2. B
3. A
4. C
5. A

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

18. THANK YOU