Q254 / 270 · NDA 2016 (Phase 1) · Mathematics
For the data
$3,5,1,6,5,9,5,2,8,6$
the mean, median and mode are $\mathrm{x}, \mathrm{y}$ and z respectively. Which one of the following is correct?
- A$x=y \neq z$
- B$x \neq y=z$
- C$x \neq y \neq z$
- Correct answerD$x=y=z$
Solution
Given data $3,5,1,6,5,9,5,2,8,6$ and mean, median and mode are $x, y, z$ respectively.
Rearranging data
$\begin{aligned}
& 1,2,3,5,5,5,6,6,8,9 \\
& \text { Mean }=x=\frac{1+2+3+5+5+5+6+6+8+9}{10}=\frac{50}{10}=5 \\
& \text { Median }=y=\frac{\frac{n^{\text {th }}}{2} \text { term }+\left(\frac{n}{2}+1\right)^{\text {th }} \text { term }}{2} \\
& y=\frac{5+5}{2}=5
\end{aligned}$
$\operatorname{Mode}(z)=$ most frequently occuring value $=5$
Hence $x=y=z$.
Hence, the correct answer is option: 'D'.