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 | 2 years ago |  101

1 Answer

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 | 2 years ago

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