Question

di is the deviation of xi from assumed mean a. If mean = x+∑fidi / ∑fi, then x is

Answer 1

$\textbf{Given:}$

$\text{ d_i is the deviation of x_i from assumed mean A and Mean =x+\dfrac{\Sigma\,f_i\,d_i}{\Sigma\,f_i} }$

$\textbf{To find:}$

$\text{x}$

$\textbf{Solution:}$

$\text{Consider,}$

$d_1=x_1-A\;\implies\;x_1=d_1+A$

$d_2=x_2-A\;\implies\;x_2=d_2+A$

.

.

.

$d_n=x_n-A\;\implies\;x_n=d_n+A$

$\text{Now,}$

$\text{Mean}=\dfrac{\Sigma\,f_ix_i}{\Sigma\,f_i}$

$\text{Mean}=\dfrac{\Sigma\,f_i(d_i+A)}{\Sigma\,f_i}$

$\text{Mean}=\dfrac{\Sigma\,f_id_i+\Sigma\,f_i\,A}{\Sigma\,f_i}$

$\text{Mean}=\dfrac{\Sigma\,f_id_i+A\Sigma\,f_i}{\Sigma\,f_i}$

$\text{Mean}=\dfrac{\Sigma\,f_id_i}{\Sigma\,f_i}+\dfrac{A\Sigma\,f_i}{\Sigma\,f_i}$

$\text{Mean}=\dfrac{\Sigma\,f_id_i}{\Sigma\,f_i}+A$

$\implies\bf\text{Mean}=A+\dfrac{\Sigma\,f_id_i}{\Sigma\,f_i}$

$\text{Comparing with \text{Mean}=x+\dfrac{\Sigma\,f_i\,d_i}{\Sigma\,f_i} , we get}$

$x=A$

$\textbf{Answer:}$

$\textbf{The value of x is A}$

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