Q54 / 150 · MHT CET 2022 (05 Aug Shift 1) · Mathematics

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 Figure Then the mean of the marks is

  • A
    $3.0$
  • B
    $2.5$
  • Correct answer
    C
    $2.8$
  • D
    $3.2$

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 $=$ $\begin{aligned} & \frac{2 \times(3+1)^2+3 \times(2 \times 3-5)+5 \times\left(3^2-3 \times 3\right)+7 \times 3}{20} \\ & =\frac{2 \times 16+3 \times 1+5 \times 0+7 \times 3}{20} \\ & =2.8\end{aligned}$

Hence, the correct answer is option: 'C'.

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