Question

Following are the marks obtained, out of 100, by two students Ravi and Hashina in 10 tests.

Ravi	25	50	45	30	70	42	36	48	35	60
Hashina	10	70	50	20	95	55	42	60	48	80

Who is more intelligent and who is more consistent?

Answer 1

Case I: For Ravi

`x_i`	`d_i = x_i = - 45`	`d_i^2`
25	– 20	400
50	5	25
45 = A	0	0
30	– 15	225
70	25	625
42	– 3	9
36	– 9	81
48	3	9
35	– 10	100
60	15	225
Total	`sumd_i = - 9`	`sumd_i^2` = 1699

∴ `sigma = sqrt((sumd_i^2)/N - ((sumd_i)/n)^2`

= `sqrt(1699/10 - ((-9)/10)^2`

= `sqrt(169.09)`

= 13.003

And `barx = A + (sumd_i)/N`

= `45 - 9/10`

= 44.1

Case II: For Hashina

`x_i`	`d_i = x_i = - 55`	`d_i^2`
10	– 45	2025
70	15	625
50	– 5	25
20	– 35	1225
95	40	1600
55 = A	0	0
42	40	169
60	5	25
48	– 7	49
80	25	625
Total	`sumd_i = - 20`	`sumd_i^2` = 6368

Assumed mean A = 55

∴ `sigma = sqrt((sumd_i^2)/N`

= `sqrt(6368/10)`

= 25.2

And `barx = A + (sumd_i)/N`

= `55 - 20/10`

= 53

For Ravi CV = `sigma/barx xx 100`

= `13.003/44.1 xx 100`

= 29.48

For Hashina CV = `sigma/barx xx 100`

= `25.2/53 xx 100`

= 47.55

Hence, Hashina is more consistent and intelligent.