Coefficient Of Variation

We are given the frequency distribution: \includegraphics[]{34.png} To calculate the coefficient of variation (CV), we use the formula:

CV%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Cmu%7D%20%5Ctimes%20100%2C

where

%5Csigma

is the standard deviation and

%5Cmu

is the mean. 1. First, calculate the mean

%5Cmu

%5Cmu%20%3D%20%5Cfrac%7B%5Csum%20f_i%20x_i%7D%7B%5Csum%20f_i%7D%20%3D%20%5Cfrac%7B1(4)%20%2B%203(3)%20%2B%205(1)%7D%7B1%20%2B%203%20%2B%205%7D%20%3D%20%5Cfrac%7B4%20%2B%209%20%2B%205%7D%7B9%7D%20%3D%20%5Cfrac%7B18%7D%7B9%7D%20%3D%202.

2. Next, calculate the variance

%5Csigma%5E2

%5Csigma%5E2%20%3D%20%5Cfrac%7B%5Csum%20f_i%20x_i%5E2%7D%7B%5Csum%20f_i%7D%20-%20%5Cmu%5E2%20%3D%20%5Cfrac%7B1(4%5E2)%20%2B%203(3%5E2)%20%2B%205(1%5E2)%7D%7B9%7D%20-%202%5E2%20%3D%20%5Cfrac%7B16%20%2B%2027%20%2B%205%7D%7B9%7D%20-%204%20%3D%20%5Cfrac%7B48%7D%7B9%7D%20-%204%20%3D%20%5Cfrac%7B48%7D%7B9%7D%20-%20%5Cfrac%7B36%7D%7B9%7D%20%3D%20%5Cfrac%7B12%7D%7B9%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D.

Thus,

%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B4%7D%7B3%7D%7D%20%3D%20%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D

. 3. Now, calculate the coefficient of variation:

CV%20%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Cmu%7D%20%5Ctimes%20100%20%3D%20%5Cfrac%7B%5Cfrac%7B2%7D%7B%5Csqrt%7B3%7D%7D%7D%7B2%7D%20%5Ctimes%20100%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%7D%7D%20%5Ctimes%20100%20%3D%20%5Cfrac%7B100%7D%7B%5Csqrt%7B3%7D%7D.

Thus, the correct answer is

%5Cfrac%7B100%7D%7B%5Csqrt%7B3%7D%7D

Chapter Questions
1 MCQs