For 20 observations of variable x,if sum(x_{i | vedclass

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

Question

(A) The standard deviation is independent of the change of origin.$	herefore$ $S$.$D$. of $x_{i} = 	ext{S.D. of } (x_{i}-2)$.Let $y_{i} = x_{i}-2$.

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The standard deviation is independent of the change of origin.$	herefore$ $S$.$D$. of $x_{i} = 	ext{S.D. of } (x_{i}-2)$.Let $y_{i} = x_{i}-2$. Then $\sum y_{i} = 20$ and $\sum y_{i}^2 = 100$ for $n = 20$.$	ext{S.D. of } y = \sqrt{\frac{\sum y_{i}^2}{n} - \left(\frac{\sum y_{i}}{n}ight)^2}$.$	ext{S.D. of } y = \sqrt{\frac{100}{20} - \left(\frac{20}{20}ight)^2}$.$	ext{S.D. of } y = \sqrt{5 - 1^2} = \sqrt{4} = 2$.Thus,the standard deviation of $x$ is $2$.

	Physics	Chemistry	Mathematics	Biology
Mean	$20$	$25$	$23$	$27$
$S$.$D$.	$3$	$2$	$4$	$5$

For $20$ observations of variable $x$,if $\sum(x_{i}-2)=20$ and $\sum(x_{i}-2)^2=100$,then the standard deviation of variable $x$ is

Similar Questions

The following table shows the information about marks obtained in Physics,Chemistry,Mathematics,and Biology by $100$ students in a class. Which subject shows the highest variability in marks?
Physics Chemistry Mathematics Biology
Mean $20$ $25$ $23$ $27$
$S$.$D$. $3$ $2$ $4$ $5$

The variance of the ungrouped data $2, 12, 3, 11, 5, 10, 6, 7$ is

The mean of $5$ observations is $15$ and variance is $9$. If two observations having values $-5$ and $13$ are combined with these observations,then what will be the new variance?

The variance of the first $50$ even natural numbers is

The standard deviation of $7$ observations $1, 2, 3, 4, 5, 6, 7$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module