If for some positive $x \hat{I} R$, the frequency distribution of the marks obtained by 20 students in a…
If for some positive $x \hat{I} R$, the frequency distribution of the marks obtained by 20 students in a certain test, is as follows
Then the mean of the marks is
$3.0$
$2.5$
$2.8$
$3.2$
Solution
Here, total number of students $=20$
$\begin{aligned} & \Rightarrow(x+1)^2+(2 x-5)+\left(x^2-3 x\right)+x=20 \\ & \Rightarrow 2 x^2+2 x-4=20 \\ & \Rightarrow x^2+x-12=0 \\ & \Rightarrow(x+4)(x-3)=0 \\ & \text { But } x=3[\text { as } x>0]\end{aligned}$
Now required mean $=$
$\begin{aligned} & \frac{2 \times(3+1)^2+3 \times(2 \times 3-5)+5 \times\left(3^2-3 \times 3\right)+7 \times 3}{20} \\ & =\frac{2 \times 16+3 \times 1+5 \times 0+7 \times 3}{20} \\ & =2.8\end{aligned}$
Then the mean of the marks is