Statistics practice · Mixed difficulty

Let the mean and variance of 12 observations be $\frac{9}{2}$ and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is $\frac{m}{n}$, where $m$ and $n$ are coprime, then $m+n$ are coprime, then $m+n$ is equal to

The point that lies on both the lines of regression for a bivariate distribution, is

Median is based on the

In a test of Statistics, marks were awarded out of 40 . The average of 15 students was 38 . Later, it was decided to give marks out of 50 . The new average marks will be

The mean of two samples of sizes 200 and 300 were found to be 25 and 10 respectively, their standard deviations were 3 and 4 respectively the variance of combined sample size of 500 is

The mode of the series 3,4,2,6,1,7,6,7,6,8,9,5 is

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and $\sigma^{2}$ respectively. If the variance of all the 30 numbers in the two sets is 13 , then $\sigma^{2}$ is equal to

The variance of the first $n$ natural numbers is

The mean of data $55,155,255,355$, 455 and 555 is

For a symmetrical distribution, the coefficient of skewness is

If the mean and the standard deviation of the data 3, 5, 7, $a$, $b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equation

The algebraic sum of the deviation of 20 observations measured from 30 is 2. Then, mean of observations is

The mean marks of students of a school is 56 . The mean marks of girls is 60 and that of boys is 50. If number of boys and girls are $n$ and $m$ respectively, then $\frac{9 n}{m}$ equals

If in a moderately skewed distribution the values of mode and mean are $6\;\lambda \;and\;9\lambda$ respectively, then the value of the median is

The mean of the series ${x_1},{x_2}, \ldots ,{x_n}$ is $\bar X.$ If ${x_2}$ is replaced by $\lambda$, then the new mean is

The mean and standard deviation of a sample of size 20 are found 10 and 2 respectively. If one item 8 is replaced by 12 then

The mean and SD of the marks of 200 candidates were found to be 40 and 15 , respectively. Later, it was discovered that a score of 40 was wrongly read as 50 . The correct mean and $\mathrm{SD}$ are respectively

In a set of $2 n$ distinct observations, each of the observations 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:

If a variable takes the discrete values $\alpha+4, \alpha-\frac{7}{2}, \alpha-\frac{5}{2}, \alpha-3, \alpha-2, \alpha+\frac{1}{2}, \alpha-\frac{1}{2}$, $\alpha+5(\alpha > 0)$, then the median is

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is

If a variable X takes values $0,1,2, \ldots ,n$ with frequencies proportional to the binomial coefficients $^n{C_0},{\;^n}{C_1},{\;^n}{C_2}, \ldots ,{\;^n}{C_n},$ then the $\mathrm{Var\;}\left( X \right)$ is

The two lines of regression are $13 x-10 y+11=0$ and $2 x-y-1=0$, then mean of $x$ and $y$ series are

If the average of the numbers 148, 146, 144, 142, ... in AP, be 125, then the total numbers in the series will be

The mean and variance for first ${n}$ natural numbers are respectively

The sum of absolute deviations about median is

For a symmetrical distribution $Q_1=20$ and $Q_3=40$. The value of 50 th percentile is

The mean square deviation of $n$ observations $x_1, x_2, \ldots, x_n$ about -2 and 2 are 18 and 10 respectively. Then S.D. of the given set is

The variance of first n natural numbers is

If the co-efficient of variation of a distribution is 60 and its standard deviation is 24, then its arithmetic mean is ____.

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