Find the mean and variance for the first $10$ multiples of $3$.
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:
The sum of squares $\sum (x_i - \bar{x})^2 = 742.5$.
Variance $(\sigma^2) = \frac{1}{n} \sum (x_i - \bar{x})^2 = \frac{742.5}{10} = 74.25$.
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
The data is obtained in tabular form as follows:
$x_i$ $60$ $61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$ $f_i$ $2$ $1$ $12$ $29$ $25$ $12$ $10$ $4$ $5$
Find the standard deviation of the given data. (in $.69$)
| $x_i$ | $60$ | $61$ | $62$ | $63$ | $64$ | $65$ | $66$ | $67$ | $68$ |
| $f_i$ | $2$ | $1$ | $12$ | $29$ | $25$ | $12$ | $10$ | $4$ | $5$ |
Find the standard deviation of the given data. (in $.69$)
Difficult
View SolutionIf $\sum_{i=1}^{10} (x_i - 15) = 12$ and $\sum_{i=1}^{10} (x_i - 15)^2 = 18$,find the standard deviation of the observations $x_1, x_2, \dots, x_{10}$.
Difficult
View SolutionIf each of the observations $x_1, x_2, \ldots, x_n$ is increased or decreased by $k$,where $k$ is a positive number,then the variance of the data:
Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?
Students of two sections $A$ and $B$ of a class show the following results in a test conducted for $100$ marks. Then
Section $A$ Section $B$ Number of students $50$ $60$ Average marks in the test $45$ $45$ Variance of distribution of marks $64$ $81$
| Section $A$ | Section $B$ | |
| Number of students | $50$ | $60$ |
| Average marks in the test | $45$ | $45$ |
| Variance of distribution of marks | $64$ | $81$ |
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo