Question

the sum of 20 observation is 300 and its sum of square is 5000 and median is 15 then find the coefficient of skew ness and coefficient of variation​

Answer 1

Answer:

CV = (sd/mean)*100

Standard deviation sd = sqrt(240/15)=sqrt(16) = 4

Mean = 20

CV = (4/20)*100 = 0.2*100 = 20

Coefficient of variation = 20

This implies that the standard deviation is 20 percentage of the mean

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Answer 2

Coefficient of skewness is 0 and coefficient of variation is 105.40  .

Step 1: Find mean and standard deviation.

Given, number of observation=20

Sum of 20 observation = 300

Sum of square = 5000

Median= 15

Mean = $\frac{sum of observation}{number of observation}$

= $\frac{300}{20}$

= $15$

Standard variation = $\sqrt{ \frac{sum of squares }{number of observation}}$

= $\sqrt{\frac{5000}{20}}$

=$\sqrt{250}$

= $15.811$

Step 2:  Find coefficient of skewness and coefficient of variation.

Coefficient of skewness = $\frac{3(mean-median)}{standard deviation}$

= $\frac{3(15-15)}{15.811}$

= $0$

Coefficient of variation = $\frac{Standard deviation}{Mean}$×$100$

= $\frac{15.811}{15}$×$100$

=$105.40$