Following is the distribution of weights of students. Compare their co

Following is the distribution of weights of students. Compare their coefficient of variations

Answer»

We get ∑x_i = 62 & ∑y_i=56

There are total 5 weight groups

∴ n =5

∴ \(\overline x = \frac {\sum x_i}{n} = \frac {62}{5} = 12.4\)

\(\overline y = \frac {\sum y_i}{n} = \frac {56}{5} = 11.2\)

Also we get \(\sum(x_i-\overline x)^2\) = 153.2 & \(\sum(y_i-\overline y)^2\) = 180.8

∴ \(\overset \sigma x = \sqrt{\frac {\sum (x_i-\overline x)^2}{n}} = \sqrt{\frac {153.2}{5}} = 5.53\)

\(\overset \sigma y = \sqrt{\frac {\sum (y_i-\overline y)^2}{n}} = \sqrt{\frac {180.8}{5}} = 6.013\)

C.V (A) = \(\frac {\overset \sigma x} {\overline x} \times 100 = \frac {5.53}{12.4} \times 100 = 44.59\)

C.V (B) = \(\frac {\overset \sigma y} {\overline y} \times 100 = \frac {6.013}{11.2} \times 100 = 53.6875\)