Find the mean and variance for: First 10 multiples of 3 - Vidyadip

Question

Find the mean and variance for: First $10$ multiples of $3$

✓

Answer

The First $10$ multiples of $3$ are given by,
$3, 6, 9, 12, 15, 18, 21, 24, 27, 30$
We know that Mean, $\overline{\mathrm{x}}=\frac{\sum_{i=1}^{\mathrm{a}} \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}$
$\therefore$ $\overline{\mathrm{x}}=\frac{3+6+9+12+15+18+21+24+27+30}{10} = \frac{165}{10} = 16.5$
From the given data, we can form the table:

$x_i$	Deviation from mean $(xi - \overline{\mathbf{X}})$	$(xi - \overline{\mathbf{X}})^2$
$3$	$3 - 16.5 = 13.5$	$182.25$
$6$	$6 - 16.5 = 10.5$	$110.25$
$9$	$9 - 16.5 = 7.5$	$56.25$
$12$	$12 - 16.5 = -4.5$	$20.25$
$15$	$15 - 16.5 = -1.5$	$2.25$
$18$	$18 - 16.5 = 1.5$	$2.25$
$21$	$21 - 16.5 = 4.5$	$20.25$
$24$	$24 - 16.5 = 7.5$	$56.25$
$27$	$27 - 16.5 = 10.5$	$110.25$
$30$	$30 - 16.5 = 13.5$	$182.25$
		$\sum_{i=1}^{10}\left(x_{i}-\bar{x}\right)^{2}$ = 742.5

We know that Variance, $\sigma^{2}=\frac{1}{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{a}}\left(\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right)^{2}$
$\therefore \sigma^{2} = (1/10) \times 742.5 = 74.25$
Mean $= 16.5$ and Variance $= 74.25$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Statistics→Statistics — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Evaluate the following limit:
Show that $\lim\limits_{\text{x}\rightarrow\infty}\big(\sqrt{\text{x}^2+\text{x}+1}-\text{x}\big)\ne\lim\limits_{\text{x}\rightarrow\infty}\big(\sqrt{\text{x}^2+1}-\text{x}\big)$

Show the following quadratic equation by factorization method:
$\sqrt{5}\text{x}^2+\text{x}+\sqrt{5}=0$

Sketch the graphs of the following curves on the same scale and the same axes:
$\text{y}=\cos\text{x}$ and $\text{y}=\cos\Big(\text{x}-\frac{\pi}{4}\Big)$

The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.

Prove the following identities:
$\sin^6\text{x}+\cos^6\text{x}=1−3\sin^2\text{x}\cos^2\text{x}$

Find the total number of ways in which six $'+'$ and four $'−'$ signs can be arranged in a line such that no two $'−'$ signs occur together.

There are $200$ individuals with a skin disorder, $120$ had been exposed to the chemical $C_1, 50$ to chemical $C_2$ and $30$ to both the chemicals $C _1$ and $C _2$. Find the number of individuals exposed to $(i)$ chemical $C _1$ but not chemical $C _2\ (ii)$ Chemical $C _2$ but not chemical $C _1\ (iii)$ Chemical $C _2$ or chemical $C _1$.

Find the sum of odd integers from 1 to 2001.

Find the equation of the straight line which joints the point $(3,5)$ to the point of intersection of lines $4 x+y=1$ and $7 x-3 y-35=0$. Prove that this line is at equal distance from origin and point $(8,34)$.

Reduce the following equations to the normal form and find p and $\alpha$ in each case:
$\text{x}-\text{y}+2\sqrt{2}=0$