JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Statistics

Let the mean and variance of 7 observations $2,4,10,x,12,14,y,x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3,\mathrm{x}-4,\mathrm{y},5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen num …

If the mean deviation about the median of the numbers $k,2k,3k,\dots ,1000k$ is 500, then $k^2$ is equal to :

Let the mean and variance of 8 numbers $-10,-7,-1,x,y,9,2,16$ be $\frac{7}{2}$ and $\frac{293}{4}$, respectively. Then the mean of 4 numbers $x,y,x+y+1,|x-y|$ is:

If the mean and the variance of the data

\begin{tabular}{|l|c|c|c|c|}
\hline Class & $4-8$ & $8-12$ & $12-16$ & $16-20$ \\
\hline Frequency & 3 & $\lambda$ & 4 & 7 \\
\hline
\end{tabular}

are $\mu$ and 19 respectively, then the value of $\lambda +\mu$ is

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99, respectively. Then $\alpha +\beta$ equals.

Let $\mathrm{X}=\{\mathrm{x}\in \mathbb{N}:1\le \mathrm{x}\le 19\}$ and for some $\mathrm{a},\mathrm{b}\in \mathbb{R}$, $\mathrm{Y}=\{\mathrm{ax}+\mathrm{b}:\mathrm{x}\in \mathrm{X}\}$. If the mean and variance of the elements of Y are 30 and 750, respectively, th …