Statistics PYQs - Last 5 Years

\(\text { The coefficient of variation for the following data is }\)
$$ \begin{array}{llllll} \hline \text { Class interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text { Frequency } & 2 & 3 & 5 & 3 & 2 \\ \hline \end{array} $$

The mean deviation about median of the numbers $3 x, 6 x, 9 x, \ldots .81 x$ is 91 , then $|x|=$

If a possion variate $X$ satisfies the relation $P(X=3)=P(X=5)$, then $P(X=4)=$

The variance of the discrete data $3,4,5,6,7,8,10,13$ is

The probability distribution of a random variable $X$ is given below. Then, the standard deviation of $X$ is
$$ \begin{array}{llllll} \hline \boldsymbol{X}=\boldsymbol{x}_1 & 2 & 3 & 5 & 7 & 12 \\ \hline \boldsymbol{P}\left(\boldsymbol{X}=\...

The mean deviation from the mean of the discrete data $2,3,5,7,11,13,17,19,22$ is

If three dice are thrown, then the mean of the sum of the numbers appearing on them is

The mean deviation from the median for the following data is
$$ \begin{array}{cllllll} x_i & 2 & 9 & 8 & 3 & 5 & 7 \\ \hline f_i & 5 & 3 & 1 & 6 & 6 & 1 \\ \hline \end{array} $$

If the variance of the numbers $9,15,21, \ldots,(6 n+3)$ is $P$, then the variance of the first $n$ even numbers is

The mean deviation about the mean for the following data is
\begin{array}{c|l|l|l|l|l}
\hline \text { Class interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\\\
\hline \text { Frequency } & 1 & 3 & 5 & 3 & 1 \\\\
\hline
\end{array}

The variance of the following continuous frequency distribution is


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The variance of the data: $1,2,3,5,8,13,17$ is approximately

The mean of a binomial variate $X \sim B(n, p)$ is 1 . If $n>2$ and $P(X=2)=\frac{27}{128}$, then the variance of the distribution is

If $M_1$ is the mean deviation from the mean of the discrete data $44,5,27,20,8,54,9,14,35$ and $M_2$ is the mean deviation from the median of the same data, then $M_1-M_2=$

The variance of the first 10 natural numbers which are multiples of 3 is

The variance of 50 observations is 7 . Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then, the variance of that new data is

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively. Later on it was found that one of the observations was taken as 50 in the place of 40 . If the wrong entry is replaced by the correct one, then ...

If the variance of the data $2,3,5,8,12$ is $\sigma^2$ and the mean deviation from the median for this data is $M$, then $\sigma^2-M=$

If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$, then $P(X=6)=$

If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1,3,5,7$, $11,13,17,19,23$, then $3\left(\sigma^2-M\right)=$

Assertion (A) The variance of the first $n$ odd natural numbers is $\frac{n^2-1}{3}$.

Reason (R) The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n\left(4 n^2-...

If 10 is the mean deviation of ' $n$ ' observations $x_1, x_2, x_3, \ldots, x_n$, then the mean deviation of the observations $\frac{2 x_1+5}{3}, \frac{2 x_2+5}{3}, \frac{2 x_3+5}{3}, \ldots . \frac{2 x_n+5}{3}$ is

Statement I The range of the ungrouped data does not change even if certain intermediate observations are removed
Statement II The value of the mean deviation of an ungrouped data about the median is always less than or equal to the value o...

The mean deviation from the mean for the observations $1,3,5,7,11,13,17,19,23$ is

There are $n$ observations and all of them are negative numbers. The ascending order of these observations is $x_1, x_2, \ldots . x_n$. If the signs of the first term and last term in that order are changed, then the range of the data is

If $\bar{x}$ is the mean of $n$ observations $x_1, x_2, \ldots ., x_n$ then the mean of the absolute deviations of these observations from $\bar{x}$ is

The mean deviation from the mean of the discrete data $1,3,4,7,11,18,29,47,78$ is