Coefficient Of Variation

We are given the frequency distribution:

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

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Coefficient Of Variation

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs