Question -
Answer -
each series. Theseries having greater C.V. is said to be more variable than the other. Theseries having lesser C.V. is said to be more consistent than the other.
Co-efficient ofvariation (C.V.) = (σ/ x̅) × 100
Where, σ = standarddeviation, x̅ = mean
For Group A
| Marks | Group A fi | Mid-point Xi | Yi = (xi – A)/h | (Yi)2 | fiyi | fi(yi)2 |
| 10 – 20 | 9 | 15 | ((15 – 45)/10) = -3 | (-3)2 = 9 | – 27 | 81 |
| 20 – 30 | 17 | 25 | ((25 – 45)/10) = -2 | (-2)2 = 4 | – 34 | 68 |
| 30 – 40 | 32 | 35 | ((35 – 45)/10) = – 1 | (-1)2 = 1 | – 32 | 32 |
| 40 – 50 | 33 | 45 | ((45 – 45)/10) = 0 | 02 | 0 | 0 |
| 50 – 60 | 40 | 55 | ((55 – 45)/10) = 1 | 12 = 1 | 40 | 40 |
| 60 – 70 | 10 | 65 | ((65 – 45)/10) = 2 | 22 = 4 | 20 | 40 |
| 70 – 80 | 9 | 75 | ((75 – 45)/10) = 3 | 32 = 9 | 27 | 81 |
| Total | 150 | | | | -6 | 342 |
Where A = 45,
and yi =(xi – A)/h
Here h = class size =20 – 10
h = 10
So, x̅ = 45 +((-6/150) × 10)
= 45 – 0.4
= 44.6
σ2 =(102/1502) [150(342) – (-6)2]
= (100/22500) [51,300– 36]
= (100/22500) × 51264
= 227.84
Hence, standarddeviation = σ = √227.84
= 15.09
∴ C.V for group A= (σ/ x̅) × 100
= (15.09/44.6) × 100
= 33.83
Now, for group B.
| Marks | Group B fi | Mid-point Xi | Yi = (xi – A)/h | (Yi)2 | fiyi | fi(yi)2 |
| 10 – 20 | 10 | 15 | ((15 – 45)/10) = -3 | (-3)2 = 9 | – 30 | 90 |
| 20 – 30 | 20 | 25 | ((25 – 45)/10) = -2 | (-2)2 = 4 | – 40 | 80 |
| 30 – 40 | 30 | 35 | ((35 – 45)/10) = – 1 | (-1)2 = 1 | – 30 | 30 |
| 40 – 50 | 25 | 45 | ((45 – 45)/10) = 0 | 02 | 0 | 0 |
| 50 – 60 | 43 | 55 | ((55 – 45)/10) = 1 | 12 = 1 | 43 | 43 |
| 60 – 70 | 15 | 65 | ((65 – 45)/10) = 2 | 22 = 4 | 30 | 60 |
| 70 – 80 | 7 | 75 | ((75 – 45)/10) = 3 | 32 = 9 | 21 | 63 |
| Total | 150 | | | | -6 | 366 |
Where A = 45,
h = 10
So, x̅ = 45 +((-6/150) × 10)
= 45 – 0.4
= 44.6
σ2 =(102/1502) [150(366) – (-6)2]
= (100/22500) [54,900– 36]
= (100/22500) × 54,864
= 243.84
Hence, standarddeviation = σ = √243.84
= 15.61
∴ C.V for group B= (σ/ x̅) × 100
= (15.61/44.6) × 100
= 35
By comparing C.V. ofgroup A and group B.
C.V of Group B >C.V. of Group A
So, Group B is morevariable.