For the data 3,5,1,6,5,9,5,2,8,6 the mean, median and mode are x, y and z respectively. Which one of the following is correct?

Correct answer: D. x=y=z Given data 3,5,1,6,5,9,5,2,8,6 and mean, median and mode are x, y, z respectively. Rearranging data aligned & 1,2,3,5,5,5,6,6,8,9 & Mean =x=(1+2+3+5+5+5+6+6+8+9)/(10)=(50)/(10)=5 & Median =y= n^ th 2 term +((n)/(2)+1)^ th term 2 & y=(5+5)/(2)=5 aligned Mode(z)= most frequently occuring value =5 Hence x=y=z .

NDA 2016

Exam: NDA
Year: 2016
Subject: Mathematics
Chapter: Statistics

NDA 2016 · Mathematics · Statistics

For the data 3,5,1,6,5,9,5,2,8,6 the mean, median and mode are x, y...

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?

Options

A $x=y \neq z$
B $x \neq y=z$
C $x \neq y \neq z$
D $x=y=z$

Correct answer

D. $x=y=z$

Step-by-step 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

Hence

x=y=z$.

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