Question

The marks obtained by $10$ students in a test are $24,30,26,15,22,20,12,25,21$and $x$ and their mean is $21$. Then the value of $x$is-

• A. $23$
• B. $18$
• C. $17$
• D. $15$

Answer 1

The correct option is D

$15$

Given

The marks obtained by $10$ students in a test are-

$24,30,26,15,22,20,12,25,21$and $x$

Sum of marks $=24+30+26+15+22+20+12+25+21+x$

$=195+x$

Total number of students $=10$

The mean of marks $=21$
We know that,

Mean $=\frac{\mathbf{S}\mathbf{u}\mathbf{m}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{m}\mathbf{a}\mathbf{r}\mathbf{k}\mathbf{s}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{s}\mathbf{t}\mathbf{u}\mathbf{d}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{s}}$

$\begin{array}{rcl}& \Rightarrow & 21=\frac{195+x}{10}\\ & \Rightarrow & 21\times 10=195+x\\ & \Rightarrow & 210=195+x\\ & \Rightarrow & x=210-195\\ & \Rightarrow & x=15\end{array}$

So, the value of $x=15$

Hence, option D is correct