Question

24. Find Bowley’s coefficient of Skewness for the following frequency distribution. No.of children per family 0 1 2 3 4 5 6 No.of families 7 10 16 25 18 11 8

Answer 1

Answer:

Skewness is a measure of symmetry. The meaning of skewness is “lack of symmetry”. Skewness gives us an idea about the concentration of higher or lower data values around the central value of the data.

For a symmetric distribution, the two quartiles namely $Q_1$ and $Q_3$ are equidistance from the median (i.e. $Q_2$). That is for symmetric distribution $Q_3 - Q_2 = Q_2 -Q_1$.

If the distriution is not symmetric (i.e., skewed) then the distance $Q_3-Q_2$ is not equal to the distance $Q_2-Q_1$. That is for asymetric distribution $Q_3-Q_2\neq Q_2-Q1$.

The absolute measure of skewness is $(Q_3-Q2)-(Q_2-Q1)= Q_3+Q_1-2*Q2$.

Step-by-step explanation:

Bowley’s coefficient of skewness is the relative measure of skewness. It is denoted by $S_b$ and is defined as

$S_b = \dfrac{Q_3+Q_1 - 2Q_2}{Q_3 -Q_1}$

The formula for $i^{th}$ quartile is

$$ \begin{aligned} Q_i=l + \bigg(\frac{\frac{iN}{4} - F_<}{f}\bigg)\times h; \quad i=1,2,3 \end{aligned} $$

where,

$l :$ the lower limit of the $i^{th}$ quartile class

$N=\sum f :$ total number of observations

$f :$ frequency of the $i^{th}$ quartile class

$F_< :$ cumulative frequency of the class previous to $i^{th}$ quartile class

$h :$ the class width