All students in a classroom performed poorly | vedclass

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

Question

(D) Let the original observations be $x_1, x_2, \dots, x_n$. The new observations after adding $10$ to each are $x_i' = x_i + 10$.Mean,median,and mode

Vedclass · Accepted Answer

Variance

Vedclass · Answer

(D) Let the original observations be $x_1, x_2, \dots, x_n$. The new observations after adding $10$ to each are $x_i' = x_i + 10$.Mean,median,and mode are measures of central tendency and they increase by $10$ when each observation is increased by $10$.However,variance is a measure of dispersion. The variance of a set of observations $x_i$ is given by $\sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2$.For the new observations,the new mean is $\bar{x}' = \bar{x} + 10$.The new variance is $\sigma'^2 = \frac{1}{n} \sum ((x_i + 10) - (\bar{x} + 10))^2 = \frac{1}{n} \sum (x_i - \bar{x})^2 = \sigma^2$.Thus,the variance remains unchanged.

Class Interval	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$2$	$3$	$4$	$1$

All students in a classroom performed poorly in mathematics. The teacher decided to increase the marks of each student by $10$. Which of the following statistical measures will not change even after adding the extra marks?

Similar Questions

If the coefficient of variation and variance of a frequency distribution are $7.2$ and $3.24$ respectively,then its mean 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

The variance of the following continuous frequency distribution is
Class Interval $0-10$ $10-20$ $20-30$ $30-40$
Frequency $2$ $3$ $4$ $1$

The mean of two samples of size $200$ and $300$ were found to be $25$ and $10$ respectively. Their standard deviations $(S.D.)$ are $3$ and $4$ respectively. Then,the variance of the combined sample of size $500$ is:

If the total number of observations is $n = 20$,$\sum x_i = 1000$ and $\sum x_i^2 = 84000$,then the variance of the distribution is

Vedclass Test Series

Exam Paper Generator

Online Exam Module