Question

From the following frequency distribution of different youngsters exercising in a gymnasium, find coefficient of skewness by Bowley’s method and state the type of skewness:

Age (years)	25	17	20	18	26	22	28	23
No. of youngsters	22	4	19	11	7	9	3	8

Answer 1

We arrange the observallon of age in ascending order.

First Quartile:

Q₁ = value of (\(\frac{n+1}{4}\))th observation

= value of (\(\frac{83+1}{4}\))th observation

= value of 21 th observation

Referring to column cf. Q₁ = 20 years

Median:

M = value of (\(\frac{n+1}{2}\))th observation

= value of (\(\frac{83+1}{2}\))th observation

= value of 42th observation

Referring to column cf, M = 22 years

Third Quartile:

Q₃ = value of 3(\(\frac{n+1}{4}\)) th observation

= value of 3 (21)th observation

= value of 63rd observation

Referring to column cf, Q₃= 25 years

Coefficient of skewness by Bowley’s Method:

Type of skewness:

j = 0.2. Therefore, the given distribution is positively skewed.