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
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
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
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