Statistics

If the mean deviation about median for the number $3,5,7,2k,12,16,21,24$arranged in the ascending order, is$6$ then the median is

Let the mean and the variance of$20$ observations $x_{1},x_{2},\ldots\,x_{20}$be$15$ and $9$, respectively. For $\alpha\,\in\,R$, if the mean of…

If the mean and the standard deviation of the data$3,5,7,a,b$ are $5$and $2$ respectively, then $a$ and $b$ are the roots of the equation:

Let $X_{1},X_{2},\ldots\,,X_{18}$ be eighteen observations such that $\underset{i=1}{\overset{18}{\sum\,}}\left(X_{i}-\alpha\,\right)=36$ and $\underset{i=1}{\overset{18}{\sum\,}}\left(X_{i}-\beta\,\right)^{2}=90$,…

The mean and variance of$10$ observations were calculated as $15$and$15$ respectively by a student who took by mistake $25$instead of $15$for one observation. Then, the correct standard deviation is _______?

The mean and standard deviation of$15$ observations are found to be$8$ and $3$respectively. On rechecking it was found that, in the observations,$20$ was misread as $5$. Then, the correct variance is equal to _____?

If the variance of the terms in an increasing $A.P.$ $b_{1}b_{2},b_{3},\ldots\,\ldots\,..,b_{11}$ is $90$ then the common difference of this $A.P.$ is

The mean and variance of $7$ observations are $8$ and $16$, respectively. If five observations are $2,4,10,12,14$ then the absolute difference of the remaining two observations is :

Let the observation $x_{i}\left(1\leq\,i\leq\,10\right)$satisfy the equations $\underset{i=1}{\overset{10}{\sum\,}}\left(x_{i}-5\right)=10$, $\underset{i=1}{\overset{10}{\sum\,}}\left(x_{i}-5\right)^{2}=40$ . If $\mu\,$…

Consider a set of $3n$ numbers having variance $4.$ In this set, the mean of first $2n$ numbers is$6$ and the mean of the remaining $n$ numbers is $3.$Anew set is constructed by adding $1$ into each of the first $2n$…

The mean and standard deviation of$40$observations are$30$and$5$respectively. It was noticed that two of these observations$12$and$10$were wrongly recorded. If$\sigma\,$is the standard deviation of the data after…

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