Consider the statistics of two sets of observations as follows :
Size | Mean | Variance | |
Observation $I$ | $10$ | $2$ | $2$ |
Observation $II$ | $n$ | $3$ | $1$ |
If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ..... .
$8$
$10$
$5$
$15$
Mean and standard deviation of 100 items are 50 and $4,$ respectively. Then find the sum of all the item and the sum of the squares of the items.
The mean and variance of $8$ observations are $10$ and $13.5,$ respectively. If $6$ of these observations are $5,7,10,12,14,15,$ then the absolute difference of the remaining two observations is
Let $\mathrm{n}$ be an odd natural number such that the variance of $1,2,3,4, \ldots, \mathrm{n}$ is $14 .$ Then $\mathrm{n}$ is equal to ..... .
Consider three observations $a, b$ and $c$ such that $b = a + c .$ If the standard deviation of $a +2$ $b +2, c +2$ is $d ,$ then which of the following is true ?
For $(2n+1)$ observations ${x_1},\, - {x_1}$, ${x_2},\, - {x_2},\,.....{x_n},\, - {x_n}$ and $0$ where $x$’s are all distinct. Let $S.D.$ and $M.D.$ denote the standard deviation and median respectively. Then which of the following is always true