Find the mean and variance for the first $10$ multiples of $3$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
The first $10$ multiples of $3$ are $3, 6, 9, 12, 15, 18, 21, 24, 27, 30$.
Here,the number of observations is $n = 10$.
The mean $\bar{x}$ is calculated as:
$\bar{x} = \frac{\sum_{i=1}^{10} x_i}{10} = \frac{3+6+9+12+15+18+21+24+27+30}{10} = \frac{165}{10} = 16.5$.
The following table shows the calculation for variance:
$x_i$ $(x_i - \bar{x})^2$
$3$ $182.25$
$6$ $110.25$
$9$ $56.25$
$12$ $20.25$
$15$ $2.25$
$18$ $2.25$
$21$ $20.25$
$24$ $56.25$
$27$ $110.25$
$30$ $182.25$

The sum of squares $\sum (x_i - \bar{x})^2 = 742.5$.
Variance $(\sigma^2) = \frac{1}{n} \sum (x_i - \bar{x})^2 = \frac{742.5}{10} = 74.25$.

Explore More

Similar Questions

Variance of first $n$ natural numbers is $\qquad$ .

The coefficient of variation of $9, 3, 11, 5, 7$ is

The arithmetic mean of marks in Mathematics for four divisions $A, B, C$ and $D$ were $80, 75, 70$ and $72$ respectively. Their standard deviations were $12, 6, 8$ and $10$ respectively. Then,which division has more uniformity?

If variables $x$ and $u$ are related by $u = \frac{x - a}{h}$,then the correct relationship between $\sigma_x$ and $\sigma_u$ is:

The mean and variance of a set of $15$ numbers are $12$ and $14$ respectively. The mean and variance of another set of $15$ numbers are $14$ and $\sigma^2$ respectively. If the variance of all the $30$ numbers in the two sets is $13$,then $\sigma^2$ is equal to $.........$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo