Question

If the mean of the given distribution is 40, then the value of x is
$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 10-20& 5\\ 20-30& 10\\ 30-40& 6\\ 40-50& x\\ 50-60& 12\\ 60-70& 4\end{array}$

• A. 7
• B. 5
• C. 10
• D. 4

Answer 1

The correct option is B 5

$\begin{array}{cccc}\text{Class interval}& x_i& \text{Frequency}\left(f_i\right)& f_i{x}_i\\ 10-20& 15& 5& 75\\ 20-30& 25& 10& 250\\ 30-40& 35& 6& 210\\ 40-50& 45& x& 45x\\ 50-60& 55& 12& 660\\ 60-70& 65& 4& 260\\ \text{Total}& & {\sum }_{i=1}^6{f}_i=37+x& {\sum }_{i=1}^6{f}_i{x}_i=1455+45x\end{array}$

Mean $\overline{x}=\frac{{\sum }_{i=1}^6{f}_1{X}_1}{{\sum }_{i=1}^6{f}_1}$

$\Rightarrow 40=\frac{1455+50x}{37+x}$
$\Rightarrow 40x+1480=45x+1455$
$\Rightarrow 5x=25$
$\Rightarrow x=5$
Then, the value of x is 5
Hence the correct answer is option b.