Question

The following frequency distribution gives the amount of annual depreciation (in lakh ₹) of 38 companies. Using this information, find skewness and its coefficient by Karl Pearson’s method. State the type of skewness.

Amount of annual depreciation (lakh ₹)	7	9	10	11 - 20	21 - 24	25 - 36
No. of companies	2	3	4	7	12	10

Answer 1

The frequency distribution of the given data is combined type. Therefore mode is not defined.

Hence, using Sk = 3 (x – M) and we calculate skewness and coefficient the formula j = 3(x¯−M)s of skewness.

Mean:

x̄ = \(\frac{Σfx}{n}=\frac{764.5}{38}\)

= ₹ 20.12 lakh

Median:

M class = class that Includes (n2)th observation

= class that includes (382)th observation

= class that includes 19th observation

Referring to column cf.

M class = 21 – 24

In exclusive form. M class = 20.5 – 24.5

Type of skewness:

S_k = – 4.14. Therefore, the given frequency distribution Is negatively skewed.