Statistics - Algebra - Mathematics Previous Year Questions

If the standard deviation of the random variable $X$ is $\sqrt{3 p q}$ and mean is $3 p$ then $E\left(x^2\right)=\ldots \ldots$

If the variance of the numbers \(2,3,11\) and \(x\) is \(\frac{49}{4}\), then the values of \(x\) are

If 1 is added to first 10 natural numbers, then variance of the numbers so obtained is

For X ~ B(n, p), if p = 0.6, E(X) = 6, then Var(X) =

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3 , ₹ 1.5 and ₹ 1. The demands for these cakes are \(20 \%, 5 \%, 10 \%, 50 \%\) and respectively, then the expected profit per cake is

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are

For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is

Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students in a class. Then subject shows the highest variability in marks

If the variance of the data 2, 4, 5, 6, 8, 17 is 23.33, then the variance of 4, 8, 10, 12, 16, 34 will be

If the standard deviation of data is 12 and mean is 72, then coefficient of variation is

For the set of 50 observations, the sum of their squares is 3050 , their arithmetic mean is 6. Hence the standard deviation of these observations is

The arithmetic mean of marks in Mathematics for four divisions A, B, C and D were \(80,75,70\) and 72 respectively. Their standard deviations were \(12,6,8\) and 10 respectively. Then, division ______ has more uniformity.

The variance and mean of 15 observations are respectively 6 and 10 . If each observation is increased by 8 then the new variance and new mean of resulting observations are respectively

Mean and variance of six observations are 8 and 16 respectively. If each observation is multiplied by 3, then new variance of the resulting observations is

The variance, for first six prime numbers greater than 5, is

If both mean and variance of 50 observations \(x_1, x_2, \ldots \ldots, x_{50}\) are equal to 16 and 256 respectively, then mean of \(\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots\left(x_{50}-5\right)^2\) is

If variance of \(x_1, x_2 \ldots \ldots, x_n\) is \(\sigma_x^2\), then the variance of \(\lambda x_1, \lambda x_2, \ldots \ldots, \lambda x_{\mathrm{n}}(\lambda \neq 0)\) is

For 20 observations of variable $x$, if \(\sum\left(x_i-2\right)=20\) and \(\sum\left(x_i-2\right)^2=100\), then the standard deviation of variable \(x\) is

The discrete random variable \(\mathrm{X}\) can take all possible integer values from 1 to \(\mathrm{k}\), each with a probability \(\frac{1}{\mathrm{k}}\), then its variance is

If the variance of the numbers \(-1,0,1, \mathrm{k}\) is 5, where \(\mathrm{k} > 0\), then \(\mathrm{k}\) is equal to