Question

The mean of following distribution is 62.8 . Find X . CI 0-20 20-40 40-60 60-80 80-100 100-120 f 5 8 X 12 7 8
DO IT IN ASSUMED MEAN METHOD .
IF YOU DO IT CORRECTLY IN ASSUMED MEAN METHOD I WILL MARK YOU AS BRAINIEST IF ANY ANSWERS NOT RELATED TO QUESTION I WILL REPORT YOU​

Answer 1

Answer:

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Answer 2

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c|c|c}\sf Class\: interval&\sf Frequency\: (f_i)&\sf \: midvalue \: (x_i)&\sf \: u_i&\sf \: f_iu_i\\\frac{\qquad  \qquad}{}&\frac{\qquad  \qquad}{}\\\sf 0 - 20&\sf 5&\sf10&\sf - 2&\sf - 10\\\\\sf 20 - 40 &\sf 8&\sf30&\sf - 1&\sf - 8\\\\\sf 40-60 &\sf x &\sf50 \: - A&\sf0&\sf0\\\\\sf 60 - 80&\sf 12&\sf70&\sf1&\sf12\\\\\sf 80-100&\sf 7&\sf90&\sf2&\sf14\\\\\sf 100-120&\sf 8&\sf110&\sf3&\sf24\\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

We have now,

$\rm :\longmapsto\:A = 50$

$\rm :\longmapsto\:h= 20$

$\rm :\longmapsto\: \sum \: f_i \: = \: 40 + x$

$\rm :\longmapsto\: \sum \: f_i u_i\: = \: 32$

and

$\rm :\longmapsto\: \bar{x} \: = \: 62.8$

We know,

Mean using Step Deviation Method is given by

$\boxed{ \bf{ \: \overline{x} \: = \: A \: + \: \frac{\sum \: f_i u_i\:}{\sum \: f_i \:} \times h}}$

So, on substituting the values in this formula, we get

$\rm :\longmapsto\:62.8 = 50 + \dfrac{32}{40 + x} \times 20$

$\rm :\longmapsto\:62.8 - 50 = \dfrac{32}{40 + x} \times 20$

$\rm :\longmapsto\:12.8 = \dfrac{32}{40 + x} \times 20$

$\rm :\longmapsto\:\dfrac{128}{10} = \dfrac{32}{40 + x} \times 20$

$\rm :\longmapsto\:\dfrac{4}{10} = \dfrac{1}{40 + x} \times 20$

$\rm :\longmapsto\:4(40 + x) = 200$

$\rm :\longmapsto\:160 + 4x = 200$

$\rm :\longmapsto\:4x = 200 - 160$

$\rm :\longmapsto\:4x = 40$

$\bf\implies \:x = 10$

Additional Information :-

1. Mean using Short Cut Method :

$\boxed{ \bf{ \: \overline{x} \: = \: A \: + \: \frac{\sum \: f_i d_i\:}{\sum \: f_i \:} }}$

2. Mean using Direct Method :-

$\boxed{ \bf{ \: \overline{x} \: = \: \frac{\sum \: f_i x_i\:}{\sum \: f_i \:} }}$