Statistics

The number of values of $a\in\mathbb N$ such that the variance of $3,7,12,a,43-a$ is a natural number is:

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38\sigma^2$ is equal to ______.

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ______.

Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\dfrac12$. A new data is constructed replacing each $x_i$ by $(x_i-i)^2$. If $\bar x$ is the mean of new data, then the greatest integer less than or equal to $\bar x$ is ______.

Let the mean and the variance of 20 observations $x_1,x_2,\dots,x_{20}$ be 15 and 9, respectively. For α ∈ R, if the mean of $(x_1+\alpha)^2,(x_2+\alpha)^2,\dots,(x_{20}+\alpha)^2$ is 178, then the square of the maximum value of α is equal to _______.

If the mean and median of the data

x	0 − 10	10 − 20	20 − 30	30 − 40	40 − 50
f	3	6	2	x	y	Σf = 20

are equal, then $xy^2$ is equal to

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is :

The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?

If the mean deviation of the numbers 1, 1 + d, ..., 1 + 100d from their mean is 255, then a value of d is :

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is :

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is ₹ 54 and per day mean wage of all the workers is ₹ 60, then per day mean wage of the night shift workers (in ₹) is :

The variance of first 50 even natural numbers is :

In a set of $2n$ distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3. Then the mean of the new set of observations :

Let $\bar X$ and M.D. be the mean and the mean deviation about $\bar X$ of n observations $x_i$, $i=1,2,\dots,n$. If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are :

Let $\bar x$, M and $\sigma^2$ be respectively the mean, mode and variance of n observations $x_1,x_2,\dots,x_n$ and $d_i=-x_i-a$, $i=1,2,\dots,n$, where a is any number.

Statement I : Variance of $d_1,d_2,\dots,d_n$ is $\sigma^2$.

Statement II : Mean and mode of $d_1,d_2,\dots,d_n$ are $-\bar x-a$ and $-M-a$, respectively