The variance of 20 observations is 5. If each | vedclass

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

Question

(B) Let the observations be $x_{1}, x_{2}, \ldots, x_{20}$ and $\bar{x}$ be their mean. Given that variance $= 5$ and $n = 20$.We know that variance $

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) Let the observations be $x_{1}, x_{2}, \ldots, x_{20}$ and $\bar{x}$ be their mean. Given that variance $= 5$ and $n = 20$.We know that variance $\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^2$.Thus,$5 = \frac{1}{20} \sum_{i=1}^{20} (x_i - \bar{x})^2$,which implies $\sum_{i=1}^{20} (x_i - \bar{x})^2 = 100$.If each observation is multiplied by a constant $k = 2$,the new observations are $y_i = 2x_i$.The new mean is $\bar{y} = 2\bar{x}$.The new variance is $\sigma_{new}^2 = \frac{1}{n} \sum_{i=1}^{n} (y_i - \bar{y})^2 = \frac{1}{20} \sum_{i=1}^{20} (2x_i - 2\bar{x})^2$.$\sigma_{new}^2 = \frac{1}{20} \sum_{i=1}^{20} 4(x_i - \bar{x})^2 = 4 	imes \left( \frac{1}{20} \sum_{i=1}^{20} (x_i - \bar{x})^2 ight) = 4 	imes 5 = 20$.Therefore,the new variance is $20$.

The variance of $20$ observations is $5$. If each observation is multiplied by $2$,find the new variance of the resulting observations.

Similar Questions

In an experiment with $15$ observations for $x$,the following results were available: $\sum x^2 = 2830$ and $\sum x = 170$. One observation $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

If $\sum_{i=1}^{n}(x_{i}-a)=n$ and $\sum_{i=1}^{n}(x_{i}-a)^{2}=na$,where $n, a > 1$,then the standard deviation of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ is

If $1$ is added to each of the first $10$ natural numbers,then the variance of the numbers so obtained is:

If the standard deviation of data is $12$ and mean is $72$,then the coefficient of variation is: (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module