For a distribution, the sum of lower and upper qualities is 50 and their difference is 10.
Find the coefficient of Q.D.
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Answer:
Sum of upper and lower quartiles (Q
1
+Q
3
)=100
Difference between upper and lower quartiles (Q
3
−Q
1
)=40
Median(Q
2
)=30
Using Q
1
+Q
3
=100...(i) &Q
3
−Q
1
=40...(ii)
the values of Q
1
&Q
3
can be found.
Adding eq
n
(i)&(ii)
Q
3
+Q
1
=100
Q
3
−Q
1
=40
⇒2Q
3
=140
⇒Q
3
=70
Now, putting the value of Q
3
in eq
n
(i)
70+Q
1
=100
⇒Q
1
=30
Now using the values of Q
1
,Q
2
&Q
3
in the formula for
Bowley's coefficient of skewness, we have,
⇒Sk
b
=
Q
3
−Q
1
Q
3
+Q
1
−2Q
2
⇒Sk
b
=
70−30
70+30−(2×30)
⇒Sk
b
=
40
40
=1
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