Where A = 45,

and y_{i} = \(
\dfrac{ (x_i – A)}{h}\)

Here h = class size = 20 – 10

h = 10

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

= 45 – 0.4

= 44.6

\( Variance(σ^2)= \)

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

σ^{2} = \( (\dfrac{10^2}{150^2}\) [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

\( Variance(σ^2)=\)

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

σ^{2} = (\( (\dfrac{10^2}{150^2}\)) [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 agoFind 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

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:

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:

Classes | 95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 |

Frequencies | 9 | 13 | 16 | 26 | 30 | 12 |

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

Classes | 0-100 | 100-200 | 200-300 | 300-400 | 400-500 | 500-600 | 600-700 | 700-800 |

Frequencies | 4 | 8 | 9 | 10 | 7 | 5 | 4 | 3 |