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  • If the variance of the frequency distribution  <img alt="x_i"

If the variance of the frequency distribution 

x_i  2  3  4  5  6  7  8

Frequency f_i

 3 6 16 \alpha 9 5 6

is 3 , then α is equal to

 

 

Option: 1

5


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer
     x_i         f_i    d_i=x_i-5 (f_i\: \: d_i)^{2} f_i\: \: d_i)f_i\: \: d_i
2 3 -3 27 -9
3 6 -2 24 -12
4 16 -1 16 -16
5 \alpha 0 0 0
6 9 1 9 9
7 5 2 20 10
8 6 3 54 18

   \begin{aligned} & \sigma^2=\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}^2}{\sum \mathrm{f}_{\mathrm{i}}}-\left(\frac{\sum \mathrm{f}_{\mathrm{i}} \mathrm{d}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}\right)^2 \\ & =\frac{150}{45+\alpha}-0=3 \\ & \Rightarrow 150=135+3 \alpha \\ & \Rightarrow 3 \alpha=15 \\ & \Rightarrow \alpha=5 \end{aligned}

Posted by

Deependra Verma

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