(D) The variance of $n$ observations is given by the formula $\sigma^2 = \frac{1}{n} \sum_{i=1}^n x_i^2 - (\bar{x})^2$,where $\bar{x}$ is the mean of

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

(D) The variance of $n$ observations is given by the formula $\sigma^2 = \frac{1}{n} \sum_{i=1}^n x_i^2 - (\bar{x})^2$,where $\bar{x}$ is the mean of the observations.Given that the mean $\bar{x} = 5$,variance $\sigma^2 = 0$,and $\sum_{i=1}^n x_i^2 = 400$.Substituting these values into the formula:$0 = \frac{1}{n}(400) - (5)^2$$0 = \frac{400}{n} - 25$$\frac{400}{n} = 25$$n = \frac{400}{25} = 16$Thus,the value of $n$ is $16$.

Class 11 Mathematics Statistics Variance and Standard Deviation

Medium

The mean and variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$ are $5$ and $0$ respectively. If $\sum_{i=1}^n x_i^2 = 400$,then the value of $n$ is equal to

AP EAMCET 2021 All AP EAMCET

A
$80$
B
$25$
C
$20$
D
$16$

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 2021 Paper All AP EAMCET years →

The mean and the standard deviation of a data set of $8$ items are $25$ and $5$ respectively. If two items $15$ and $25$ are added to this data,then the variance of the new data is:

MediumAP EAMCET 2018

View Solution

For a given distribution of marks,the mean is $35.16$ and its standard deviation is $19.76$. The coefficient of variation is:

Easy

View Solution

If $\sum_{i=1}^9(x_i-5)=9$ and $\sum_{i=1}^9(x_i-5)^2=45$,then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

MediumAP EAMCET 2025

View Solution

Let one angle of a triangle be $60^{\circ}$. If the variance of the three angles of the triangle is $4614^{\circ}$,then the other two angles are

MediumAP EAMCET 2021

View Solution

If $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?

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

The mean and variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$ are $5$ and $0$ respectively. If $\sum_{i=1}^n x_i^2 = 400$,then the value of $n$ is equal to

Similar Questions

The mean and the standard deviation of a data set of $8$ items are $25$ and $5$ respectively. If two items $15$ and $25$ are added to this data,then the variance of the new data is:

For a given distribution of marks,the mean is $35.16$ and its standard deviation is $19.76$. The coefficient of variation is:

If $\sum_{i=1}^9(x_i-5)=9$ and $\sum_{i=1}^9(x_i-5)^2=45$,then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

Let one angle of a triangle be $60^{\circ}$. If the variance of the three angles of the triangle is $4614^{\circ}$,then the other two angles are

If $x_1, x_2, ..., x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 100$,then which of the following is a possible value of $n$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module