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

Asked by Abhisek | 1 year ago |  76

##### Solution :- Where A = 45,

and yi = $$\dfrac{ (x_i – A)}{h}$$

Here h = class size = 20 – 10

h = 10

So, x̅ = 45 + (($$\dfrac{-6}{150}$$) × 10)

= 45 – 0.4

= 44.6

$$Variance(σ^2)=$$

$$\dfrac{h^2}{N^2}[N\displaystyle\sum{f_i}y_i^2-(\displaystyle\sum{f_i}y_i)^2]$$

σ2 = $$(\dfrac{10^2}{150^2}$$ [150(342) – (-6)2]

= ($$\dfrac{100}{22500}$$) [51,300 – 36]

= ($$\dfrac{100}{22500}$$) × 51264

= 227.84

Hence, standard deviation = σ

$$\sqrt{227.84}$$

= 15.09

C.V for group A = $$\dfrac{σ}{x̅}$$ × 100

= ($$\dfrac{15.09}{44.6}$$) × 100

= 33.83

Now, for group B. Where A = 45,

h = 10

So, x̅ = 45 + (($$\dfrac{-6}{150}$$) × 10)

= 45 – 0.4

= 44.6

$$Variance(σ^2)=$$

$$\dfrac{h^2}{N^2}[N\displaystyle\sum{f_i}y_i^2-(\displaystyle\sum{f_i}y_i)^2]$$

σ2 = ($$(\dfrac{10^2}{150^2}$$) [150(366) – (-6)2]

= ($$\dfrac{100}{22500}$$) [54,900 – 36]

= ($$\dfrac{100}{22500}$$) × 54,864

= 243.84

Hence, standard deviation = σ

$$\sqrt{ 243.84}$$

= 15.61

C.V for group B = ($$\dfrac{σ}{x̅}$$) × 100

= ($$\dfrac{15.61}{44.6}$$) × 100

= 35

By comparing C.V. of group A and group B.

C.V of Group B > C.V. of Group A

So, Group B is more variable.

Answered by Pragya Singh | 1 year ago

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