Bowley skewness 1

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 54

2. RECAP
• Karl Pearson's Co-efficient of Skewness Under
Continuous Series Problems---------02

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 - 54
• Bowely's Co-efficient of Skewness Under Individual
and Discrete Series Problems----------------02

6. Bowley’s Co-efficient of Skewness
In Karl Pearson method of measuring skewness the
whole of the series is needed. Prof. Bowley has
suggested a formula based on position of quartiles. In
symmetric distribution quartiles will be equidistance
from the median. Q2 – Q1 = Q3 – Q2 , but in skewed
distributions it may not happen. Hence
Q3 + Q1 – 2Median OR Q2
SK = Q3 – Q1

7. CONTD
Ex ; 1. Calculate Bowley’s skewness under individual
series; 10,15,20,25,30,35,40,
Calculation of Bowely’s skewness
10,15,20,25,30,35,40, N = 7
Q1= size of (N+1/4) = (7+1/4) = 8/4= 2nd item, Q1 = 15
Q3 = size of 3(N+1/4) = 3(7+1/4) = 3(8)/4 = 24/4
Q3 = 24/4 , 6th item Q3 = 35
Median = size of N+1/2 = 7+1/2= 8/2 = 4th item
Median = 25
Q3 + Q1 – 2Median OR Q2
SK = Q3 – Q1 = 35 + 15 – 2x25
35 - 15
SK = 00

8. CONTD
Ex; 2.Calculate Bowley’s skewness under discrete series
Ans; Here, quartiles can be calculated:
After calculating less than cumulative frequency (L.C.f)
Qj class = size of j(N+1/4) th item ; j = 1, 2, 3

9. CONTD
Q3 +Q1 – 2Median
SK = Q3 – Q1 OR

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

11. MCQs
1 .The distribution in sum of Q3+Q1= 44,Q3–Q1= 16 and
median = 21, bowley skewness
a) 0.125
b) Positive skewed
c) Negative skewed
d) None of these
2. formula of Bowley’s of skewness
a) Sk= Q3+ Q1 – 2median/ Q3 – Q1
b) Negatively skewed
c) Symmetrical
d) None of these

12. 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

13. 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

14. CONTD
ANSWERS
1. A
2. A
3. A
4. C
5. A

15. 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

16. THANK YOU