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 two observations is

The cumulative distribution function of a discrete random variable X is given by

Then $\mathrm{E(X^2)=}$

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

then the mean of the marks is

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 wrong and was replaced by the correct value 30 . Then the corrected variance is

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 remaining two observations is

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

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 observations is

If X is a random variable with distribution given below

Then the value of $k$ and its variance are respectively given by

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 $q$, where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values, then $q$ is equal to

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 remaining two observations is

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, then the standard deviation of marks in six tests is

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, then value of $n$ is

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

A random variable $X$ has the following probability distribution

The mean and variance of X are respectively

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 $$\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots,\left(x_{50}-5\right)^2$$ is

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. $$f(x)$$

$$f(x)=\left\{\begin{array}{cl}12 x^2(1-x), & \text { if } 0< x <1 \\ 0 ; & \text { otherwise }\end{array}\right.$$ is

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 $$\sigma^2$$ are mean and variance of $$x_{\mathrm{i}}, \mathrm{i}=1,2, \ldots \ldots \mathrm{n}$$, then $$\sigma^2$$ 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

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

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 $$\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots\left(x_{50}-5\right)^2$$ 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

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 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

is

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

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.

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 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

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 $$20 \%, 5 \%, 10 \%, 50 \%$$ and respectively, then the expected profit per cake is

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

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 $E\left(x^2\right)=\ldots \ldots$