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

### Related Questions

#### Find the mean deviation from the mean and from a median of the following distribution

Find the mean deviation from the mean and from a median of the following distribution:

 Marks 0-10 10-20 20-30 30-40 40-50 No. of students 5 8 15 16 6

#### The age distribution of 100 life-insurance policy holders is as follows:

The age distribution of 100 life-insurance policy holders is as follows

 Age (on nearest birthday) 17-19.5 20-25.5 26-35.5 36-40.5 41-50.5 51-55.5 56-60.5 61-70.5 No. of persons 5 16 12 26 14 12 6 5

#### Compute mean deviation from mean of the following distribution:

Compute mean deviation from mean of the following distribution:

 Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of students 8 10 15 25 20 18 9 5

#### Find the mean deviation from the mean for the following data

Find the mean deviation from the mean for the following data:

 Classes 95-105 105-115 115-125 125-135 135-145 145-155 Frequencies 9 13 16 26 30 12