Statistics · Mathematics · MHT CET

The mean and variance of seven observations are 8 and 16 respectively. If five of the observations are $2,4,10,12,14$, then the product of remaining t...

The cumulative distribution function of a discrete random variable X is given by .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-colo...

If the sum of the deviations of 50 observations from 30 is 50 , then the mean of these observations is

Variance of first n natural numbers is ________.

The mean of the numbers $a, b, 8,5,10$ is 6 and the variance is $6.8$ . Then which of the following gives possible values of $a$ and $b$ ?

 If for some $x \in \mathbb{R}^{+} \cup\{0\}$, the frequency distribution of the marks obtained by 20 students in a test is .tg {border-collapse:col...

In an experiment with 15 observations for $x$, the following results were available $\sum x^2=2830, \sum x=170$. One observation 20 was found to be wr...

The mean and variance of 7 observations are 8 and 16 respectively. If first five observations are $2,4,10,12,14$, then absolute difference of remainin...

Mean and variance of six observations are 6 and 12 respectively. If each observation is multiplied by 3, then new variance of the resulting observatio...

The variance of 20 observations is 5 . If each observation is multiplied by 3 and then 8 is added to each number, then variance of resulting observati...

If X is a random variable with distribution given below .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:soli...

The mean and the standard deviation of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by...

The mean and variance of seven observations are 8 and 16 respectively. If 5 of the observations are $2,4,10,12,14$, then the square root of product of...

The variance of first 50 even natural numbers is

A student scores the following marks in five tests : $54,45,41,43,57$. His score is not known for the sixth test. If the mean score is 48 in six tests...

The mean of $n$ observations is $\bar{x}$. If three observations $\mathrm{n}+1, \mathrm{n}-1,2 \mathrm{n}-1$ are added such that mean remains same, th...

Consider three observations $\mathrm{a}, \mathrm{b}$ and c such that $b=a+c$. If the standard deviation of $\mathrm{a}+2, \mathrm{~b}+2, \mathrm{c}+2$...

A random variable $X$ has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-s...

The mean of 100 observations is 50 and their standard deviation is 5 , then the sum of all squares of all the observations is

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

The variance of 20 observations is 5. If each observation is multiplied by 2, then variance of resulting observations is

Variance of first $$2 n$$ natural numbers is

If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then the value of $$p$$ is

The c.d.f. $$F(x)$$ associated with p.d.f. $$f(x)$$ $$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0...

The raw data $$x_1, x_2, \ldots \ldots, x_{\mathrm{n}}$$ is an A.P. with common difference $$\mathrm{d}$$ and first term $$0, \bar{x}$$ and $$\sigma^2...

The discrete random variable $$\mathrm{X}$$ can take all possible integer values from 1 to $$\mathrm{k}$$, each with a probability $$\frac{1}{\mathrm{...

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 $$...

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

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\righ...

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...

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

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

If the mean and S.D. of the data $$3,5,7, a, b$$ are 5 and 2 respectively, then $$a$$ and $$b$$ are the roots of the equation

A random variable $$\mathrm{X}$$ assumes values 1, 2, 3, ....., n with equal probabilities, if $$\operatorname{var}(X)=E(X)$$, then $$\mathrm{n}$$ is...

The standard deviation of the following distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;b...

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 resul...

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 $$1...

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

140. Given that total of 16 values is 528 and sum of the squares of deviation from 33 is 9158. The variance is

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

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

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 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...

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...

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

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