1.From the data given below state which group is more variable, A or B?
Marks | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Group A | 9 | 17 | 32 | 33 | 40 | 10 | 9 |
Group B | 10 | 20 | 30 | 25 | 43 | 15 | 7 |
The group having a higher coefficient of variation will be more variable.
Let the assumed mean, A = 45 and h = 10
For Group A
Marks |
Group A
|
Midpoint
|
|
|||
10-20 | 9 | 15 | -3 | 9 | -27 | 81 |
20-30 | 17 | 25 | -2 | 4 | -34 | 68 |
30-40 | 32 | 35 | -1 | 1 | -32 | 32 |
40-50 | 33 | 45 | 0 | 0 | 0 | 0 |
50-60 | 40 | 55 | 1 | 1 | 40 | 40 |
60-70 | 10 | 65 | 2 | 4 | 20 | 40 |
70-80 | 9 | 75 | 3 | 9 | 27 | 81 |
=N = 150 |
|
= -6 |
=342 |
Mean,
We know, Variance,
We know, Standard Deviation =
Coefficient of variation =
C.V.(A) =
Similarly,
For Group B
Marks |
Group A
|
Midpoint
|
|
|||
10-20 | 10 | 15 | -3 | 9 | -30 | 90 |
20-30 | 20 | 25 | -2 | 4 | -40 | 80 |
30-40 | 30 | 35 | -1 | 1 | -30 | 30 |
40-50 | 25 | 45 | 0 | 0 | 0 | 0 |
50-60 | 43 | 55 | 1 | 1 | 43 | 43 |
60-70 | 15 | 65 | 2 | 4 | 30 | 60 |
70-80 | 7 | 75 | 3 | 9 | 21 | 72 |
=N = 150 |
|
= -6 |
=375 |
Mean,
We know, Variance,
We know, Standard Deviation =
Coefficient of variation =
C.V.(B) =
Since C.V.(B) > C.V.(A)
Therefore, Group B is more variable.