The mean and standard deviation of a group of | vedclass

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

Question

(B) Given $n = 100$,$\bar{x} = 20$,$\sigma = 3$.Sum of observations $\sum x_i = 100 	imes 20 = 2000$.Sum of squares of observations $\sum x_i^2 = n(\

Vedclass · Accepted Answer

Mean $= 20.1$,Standard Deviation $= 3.02$

Vedclass · Answer

(B) Given $n = 100$,$\bar{x} = 20$,$\sigma = 3$.Sum of observations $\sum x_i = 100 	imes 20 = 2000$.Sum of squares of observations $\sum x_i^2 = n(\sigma^2 + \bar{x}^2) = 100(3^2 + 20^2) = 100(9 + 400) = 40900$.Incorrect observations are $21, 21, 18$. Sum $= 60$. Sum of squares $= 21^2 + 21^2 + 18^2 = 441 + 441 + 324 = 1206$.New $n = 100 - 3 = 97$.New sum $\sum x_i' = 2000 - 60 = 1940$.New mean $\bar{x}' = \frac{1940}{97} = 20$.New sum of squares $\sum x_i'^2 = 40900 - 1206 = 39694$.New variance $\sigma'^2 = \frac{\sum x_i'^2}{n'} - (\bar{x}')^2 = \frac{39694}{97} - 20^2 = 409.216 - 400 = 9.216$.New standard deviation $\sigma' = \sqrt{9.216} \approx 3.036$.

Variate $x$	$1$	$2$	$3$	$4$	$5$
Freq $f$ of $x$	$4$	$5$	$y$	$1$	$2$

The mean and standard deviation of a group of $100$ observations were found to be $20$ and $3$,respectively. Later on,it was found that three observations were incorrect,which were recorded as $21, 21,$ and $18$. Find the mean and standard deviation if the incorrect observations are omitted.

Similar Questions

The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1, 3, 5$,then the sum of cubes of the remaining two observations is

Find the least positive value of $k$,if the range of $15, 14, k, 25, 30, 35$ is $23$.

The average weight of students in a class of $35$ students is $40 \ kg$. If the weight of the teacher is included,the average weight increases by $0.5 \ kg$. The weight of the teacher is.....$kg$.

If the mean of the distribution is $2.6$,then the value of $y$ is:
Variate $x$ $1$ $2$ $3$ $4$ $5$
Freq $f$ of $x$ $4$ $5$ $y$ $1$ $2$

Vedclass Test Series

Exam Paper Generator

Online Exam Module