Statistics

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…

Let the mean and standard deviation of marks of class A of $100$students be respectively $40$ and $\alpha\,\left(>0\right)$, and the mean and standard deviation of marks of class $B$ of $n$ students be respectively $55$…

Let the mean and the variance of seven observations $2, 4, \alpha, 8, \beta, 12, 14$, $\alpha<\beta$, be $8$ and $16$ respectively. Then the quadratic equation whose roots are $3\alpha + 2$ and $2\beta + 1$ is :

Let $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{N}$ and $\mathrm{a} < \mathrm{b} < \mathrm{c}$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $9,25, \mathrm{a}, \mathrm{b},…

The mean of $6$ distinct observations is $6.5$and their variance is $10.25.$ If$4$ out of $6$ observations are $2,4,5$and $7,$ then the remaining two observations are:

Let the mean and variance of$8$numbers$x,y,10,12,6,12,4,8$be$9$and$9.25$respectively. If$x>y,$then$3x-2y$is equal to$\_\_\_\_\_\_\_$

If the mean and variance of the data $65,68,58,44$, $48,45,60,\alpha\,,\beta\,,60$where $\alpha\,>\beta\,$ are $56$ and $66.2$ respectively, then $\alpha\,^{2}+\beta\,^{2}$is equal to

The mean deviation about the mean for the data $x_i$ $5$ $7$ $9$ $10$ $12$ $15$ $f_i$ $8$ $6$ $2$ $2$ $2$ $6$ is equal to:

If the mean and the variance of the data \(\begin{array}{|c|c|c|c|c|} \hline \text{Class} & 4\text{-}8 & 8\text{-}12 & 12\text{-}16 & 16\text{-}20 \\ \hline \text{Frequency} & 3 & \lambda & 4 & 7 \\ \hline \end{array}\)…

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.80$. Then which one of the following gives possible values of $a$ and $b$ ?

The mean and standard deviation of 20 observations are found to be 10 and 2 . respectively. On rechecking, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is