KPC skewness 2

1. PROGRAMME B.COM
SUBJECT
QUANTITATIVE TECHNIQUE – I
SEMESTER III
UNIVERSITY VIJAYANAGAR SRI
KRISHNADEVARAYA UNIVERSITY,
BALLARI
SESSION 55

2. RECAP
• Bowely's Co-efficient of Skewness Under Individual
and Discrete 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 - 55
• Bowely's Co-efficient of Skewness Under Continuous
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
Calculate Bowley’s co efficient of skewness, Ex;1
ANS; Q3 + Q1 – 2Median OR Q2
SK = Q3 – Q1
To compute quartiles, Qj class = (Nth/4) item

8. CONTD

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

10. CONTD
Bowley's coefficient of skewness :
Q3 +Q1 – 2Median
SK = Q3 – Q1
OR

11. CONTD
Ex; 2, Find out Bowley's coefficient of skewness :
ANS; the above data is given in inclusive method, we
should convert into exclusive method by the help of
correction factor. Ex, Lower limit of Second Class is 70 &
Upper limit of first Class is 60.
Correction Factor = 70 – 60/ 2
Correction Factor = 0 .5
Subtract CF in all lower limits and add to all upper limits,
we get, SEE IN NEXT SLIDE

12. CONTD
Calculation of Bowley skewness
Q3 + Q1 – 2Median OR Q2
SK = Q3 – Q1

13. CONTD

14. CONTD
Bowley's coefficient of skewness :
Q3 + Q1 – 2Median OR Q2
SK = Q3 – Q1

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

16. 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

17. 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

18. 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

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

20. 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

21. THANK YOU