Question

In the formula of mean, $\overline{x}=A+\frac{\sum f_i{d}_i}{\sum f_i},d_i=$....................

• A. $f_i-A$
• B. $A-x_i$
• C. $A-f$
• D. $x_i-A$

Answer 1

Answer: (D)

$x_i-A$

$\overline{x}=A+\frac{\sum f_i{d}_i}{\sum f_i}$

As per definition, the mean $\overline{x}$ can be written as $\frac{\sum f_i{x}_i}{\sum f_i}$

Equating the two values of $\overline{x}$, we have

$\frac{\sum f_i{x}_i}{\sum f_i}=A+\frac{\sum f_i{d}_i}{\sum f_i}$

Multiplying throughout by $\sum f_i$, we have

$\sum f_i{x}_i=A\times \sum f_i+\sum f_i{d}_i$

Since $A$ is a constant, $\sum f_i{x}_i=\sum f_{i}A+\sum f_i{d}_i$

$\Rightarrow \sum f_i{x}_i=\sum f_i(A+d_i)$

$\Rightarrow x_i=A+d_i$

$\therefore d_i=x_i-A$