Question

The students of two groups A and B obtained following marks in a test of Mathematics.

Find which group gave more consistent performance, based on coefficient of range.

Marks of Group A 35 47 42 45 40 39 38 46 41 43

Marks of Group B 35 70 55 65 60 42 73 80 53 57

4. The temperatures recorded at the end of every 4 hours during a day at two cities Mumbai

and Pune are given below:

Mumbai 28 30 34 31 28 27

Pune 25 28 34 40 32 26

Use appropriate measure of dispersion and comment on variation.

Answer 1

3.

Coefficient of Range:

$k=\frac{f_{max}-f_{min}}{f_{max}+f_{min}}$

for Group A:

$k_1=\frac{47-35}{47+35}=0.146$

for Group B:

$k_2=\frac{80-35}{80+35}=0.391$

since $k_1<k_2$ , Group A has more consistent performance

4.

standard deviation:

$s=\sqrt{\frac{\sum (x_i-\overline{x})^2}{n-1}}$

for Mumbai:

$s_1=2.582$

for Pune:

$s_2=5.672$

since $s_1<s_2$ , we can conclude that dispersion of temperature around mean value

is more for Pune