If the total number of observations is 20, x_ i =1000 and x_ i^2=84000 , then what is the variance of the distribution?

Correct answer: C. 1700 Total no. of observation (n)=20 aligned & x_i=1000 & x =( x_i)/(n)=(1000)/(20)=50 & Variance =s d^2 & s d= (1)/(n) x_i^2-( x )^2 & (s d)^2=(1)/(n) x_i^2-( x )^2=(84000)/(20)-(50)^2 & =4200-2500=1700 & Variance =1700 aligned

NDA 2016

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

NDA 2016 · Mathematics · Statistics

If the total number of observations is 20, x_ i =1000 and x_...

If the total number of observations is

20, \Sigma \mathrm{x}_{\mathrm{i}}=1000

and

\Sigma \mathrm{x}_{\mathrm{i}^2=84000

, then what is the variance of the distribution?

Options

A $1500$
B $1600$
C $1700$
D $1800$

Correct answer

C. $1700$

Step-by-step solution

Total no. of observation

(n)=20

\begin{aligned} & \Sigma x_i=1000 \\ & \bar{x}=\frac{\Sigma x_i}{n}=\frac{1000}{20}=50 \\ & \text{ Variance }=s d^2 \\ & s d=\sqrt{\frac{1}{n} \Sigma x_i^2-(\bar{x})^2} \\ & (s d)^2=\frac{1}{n} \Sigma x_i^2-(\bar{x})^2=\frac{84000}{20}-(50)^2 \\ & \quad=4200-2500=1700 \\ & \text{ Variance }=1700 \end{aligned}

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