Find Bowley’s coefficient of skewness for the following data

To know the Bowley’s coefficient of skewness, we need to calculate three quartiles they are \$N / 4 , N / 2 ,(3N) / 4\$

Bowley’s coefficient of skewness formula sk = \$(Q_3 + Q_1 - 2Q_2) / (Q_3 - Q_1)\$

Total frequency

N = 80

class intervel

h = 1

First quartile Q_1 = \$"value of" (N/4)^(th) "observation"\$

simplification of first quartile

\$Q_1\$ = \$80/4\$ = 20

From the c.f \$20^(th)\$ observation. The 20^(th) value is 1

Second quartile \$Q_2\$ = \$"value of" (N/2)^(th) "observation"\$

simplification of second quartile

\$Q_2\$ = \$80/2\$ = 40

From the c.f \$40^(th)\$ observation. The 40^(th) value is 2

Third quartile \$Q_3\$ = \$"value of" ((3N)/4)^(th) "observation"\$

simplification of third quartile

\$Q_3\$ = \$(3*80)/4\$ = 60

From the c.f \$60^(th)\$ observation. The 60^(th) value is 4

Bowley’s coefficient of skewness formula sk = \$(Q_3 + Q_1 - 2Q_2) / (Q_3 - Q_1)\$

simplification

sk = \$(4 + 1 - 2(2)) / (4 - 1)\$

simplification

sk = \$(5 - 4) / 3\$

After simplification we get

sk = 0.33

Answer

C