(C) Let the first distribution be $X$ with values $x_i$ and frequencies $f_i$. The variance is given by $\sigma_X^2 = 45.8$.The second distribution $Y

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Let the first distribution be $X$ with values $x_i$ and frequencies $f_i$. The variance is given by $\sigma_X^2 = 45.8$.The second distribution $Y$ has values $y_i$ where $y_i = 2x_i + 2$.We know that if $Y = aX + b$,then the variance $\sigma_Y^2 = a^2 \sigma_X^2$.In this case,$y_i = 2x_i + 2$,so $a = 2$.Therefore,$\sigma_Y^2 = 2^2 \times \sigma_X^2 = 4 \times 45.8$.$\sigma_Y^2 = 183.2$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

$y_i$ $10$ $18$ $24$ $36$ $42$ $50$ $66$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

$y_i$	$10$	$18$	$24$	$36$	$42$	$50$	$66$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

AP EAMCET 2018 All AP EAMCET

A
$93.6$
B
$\sqrt{93.9}$
C
$183.2$
D
$\sqrt{183.2}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Statistics

Subtopic

Variance and Standard Deviation

Previous Year

AP EAMCET 2018 Paper All AP EAMCET years →

The mean square deviation of a set of observations $x_1, x_2, \dots, x_n$ about a point $c$ is defined as $\frac{1}{n} \sum_{i=1}^n (x_i - c)^2$. If the mean square deviations about $-2$ and $2$ are $18$ and $10$ respectively,find the standard deviation of this set of observations.

Difficult

View Solution

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 $64$ $81$

EasyAP EAMCET 2023

View Solution

Find the mean and variance for the following frequency distribution:

Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $150-180$ $180-210$

$f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

Difficult

View Solution

Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

EasyTS EAMCET 2018

View Solution

Let the observations $x_{i} (1 \leq i \leq 10)$ satisfy the equations $\sum_{i=1}^{10}(x_{i}-5)=10$ and $\sum_{i=1}^{10}(x_{i}-5)^{2}=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_{1}-3, x_{2}-3, \dots, x_{10}-3$,then the ordered pair $(\mu, \lambda)$ is equal to:

DifficultJEE MAIN 2020

View Solution

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

	Section $A$	Section $B$
Number of students	$50$	$60$
Average marks in the test	$45$	$45$
Variance of distribution of marks	$64$	$81$

Classes	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$	$180-210$
$f_i$	$2$	$3$	$5$	$10$	$3$	$5$	$2$

If the variance of the distribution is $45.8$,then find the variance of the distribution given below: $x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$ $f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$ $y_i$ $10$ $18$ $24$ $36$ $42$ $50$ $66$ $f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

Similar Questions

The mean square deviation of a set of observations $x_1, x_2, \dots, x_n$ about a point $c$ is defined as $\frac{1}{n} \sum_{i=1}^n (x_i - c)^2$. If the mean square deviations about $-2$ and $2$ are $18$ and $10$ respectively,find the standard deviation of this set of observations.

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 $64$ $81$

Find the mean and variance for the following frequency distribution: Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $150-180$ $180-210$ $f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$

Let $\sigma_1$ and $\sigma_2$ be the standard deviations of two distributions $D_1$ and $D_2$ respectively,and $D_1$ be more consistent than $D_2$. If the means of $D_1$ and $D_2$ are the same,then the percentage increase in the standard deviation of $D_2$ over the standard deviation of $D_1$ is:

Let the observations $x_{i} (1 \leq i \leq 10)$ satisfy the equations $\sum_{i=1}^{10}(x_{i}-5)=10$ and $\sum_{i=1}^{10}(x_{i}-5)^{2}=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_{1}-3, x_{2}-3, \dots, x_{10}-3$,then the ordered pair $(\mu, \lambda)$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$ $4$ $8$ $11$ $17$ $20$ $24$ $32$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

$y_i$ $10$ $18$ $24$ $36$ $42$ $50$ $66$

$f_i$ $3$ $5$ $9$ $5$ $4$ $3$ $1$

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 $64$ $81$

Find the mean and variance for the following frequency distribution:

Classes $0-30$ $30-60$ $60-90$ $90-120$ $120-150$ $150-180$ $180-210$

$f_i$ $2$ $3$ $5$ $10$ $3$ $5$ $2$