The mean and the standard deviation (s.d.) of | vedclass

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

Question

(C) Given that the mean $\bar{x} = 9$ and standard deviation $\sigma = 0$ for $n = 5$ observations.Since $\sigma = 0,$ all five observations must be e

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(C) Given that the mean $\bar{x} = 9$ and standard deviation $\sigma = 0$ for $n = 5$ observations.Since $\sigma = 0,$ all five observations must be equal to the mean.Thus,the observations are $9, 9, 9, 9, 9.$Let the new observation be $x_5'$ after changing one value. The sum of the other four observations is $9 	imes 4 = 36.$The new mean is given as $10,$ so $\frac{36 + x_5'}{5} = 10.$$36 + x_5' = 50 \Rightarrow x_5' = 14.$The new set of observations is $9, 9, 9, 9, 14.$The new standard deviation $\sigma_{new} = \sqrt{\frac{\sum (x_i - \bar{x}_{new})^2}{n}}.$$\sigma_{new} = \sqrt{\frac{4(9 - 10)^2 + (14 - 10)^2}{5}} = \sqrt{\frac{4(1) + 16}{5}} = \sqrt{\frac{20}{5}} = \sqrt{4} = 2.$

Marks of $A$	$30, 20, 40$
Marks of $B$	$70, 0, 5$

The mean and the standard deviation $(s.d.)$ of five observations are $9$ and $0,$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10,$ then their $s.d.$ is?

Similar Questions

If the median of the data $6, 7, x-2, x, 18$ and $21$ written in ascending order is $16$,then the variance of that data is

The variance of the first $n$ natural numbers is

The variance for the first six prime numbers greater than $5$ is

The marks obtained by students $A$ and $B$ in $3$ examinations are given below:

Marks of $A$ $30, 20, 40$

Marks of $B$ $70, 0, 5$

The ratio of the coefficient of variation of marks of $A$ and the coefficient of variation of marks of $B$ is:

Find the coefficient of variation for the given observations: $10, 14, 11, 9, 8, 12, 6$. (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module