Question

For a set of 100 observations, taking assumed mean as 4, the sum of the deviations is -11 cm, and the sum of the squares of these deviations is 275 $cm^2$. Find the coefficient of variation.

Answer 1

42.6%

Answer 2

Let the number of observations be $n = 100$.

The actual mean is found by correcting the assumed mean with the average deviation:

$$\bar{x} = 4 + \frac{-11}{100} = 4 - 0.11 = 3.89 \, \text{cm}$$

The variance is given by:

$$\sigma^2 = \frac{\sum (x-4)^2}{n} = \frac{275}{100} = 2.75 \, \text{cm}^2$$

Thus, the standard deviation is:

$$\sigma = \sqrt{2.75} \approx 1.658 \, \text{cm}$$

The coefficient of variation (CV) is:

$$\text{CV} = \left(\frac{\sigma}{\bar{x}}\right) \times 100 = \left(\frac{1.658}{3.89}\right) \times 100 \approx 42.63\%$$