Statistics practice · Easy

The correlation between two variables $x$ and $y$ is given to be $r$. The values of $x$ and $y$ change such that $\operatorname{Cov}(x, y)$ remains unaltered and $\operatorname{Var}(x)$ and $\operatorname{Var}(y)$ are changed to four times their original values. The new correlation coefficient is changed to

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

Median of $16,10,14,11,9,8,12,6,5$ is

The mean of 100 items is 49 . It was later discovered that three items taken as $40,20,50$ were actually 60 , 70,80 , respectively. The correct mean is

The marks of some students were listed out of 75. The SD of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is

The coefficient of correlation between $x$ and $y$ is 0.5 and their covariance is 16 and SD of $x$ is 4 , then SD of $y$ is

If the lines of regression of ${Y}$ on ${X}$ and ${X}$ on ${Y}$ are respectively $y={K} x+4$ and $x=4 y+5$, then

If the standard deviation of the numbers $- 1,\,0,\,1,\,k$ is $\sqrt 5$ where $k > 0$, then $k$ is equal to

Consider three observations $a,\,b$ and $c$ such that $b\, = \,a\, + \,c$. If the standard deviation of $a\, + \,2,\,b\, + \,2c,\,c\, + \,2$ is $d$, then which of the following is true?

The arithmetic mean of the series $1,2,2^2, \ldots, 2^{n-1}$ is

If the value of mode and mean is 60 and 66 respectively, then the value of median is-

If the lines of regression are $3x + 12y = 19\;\mathrm{and}\;3y + 9x = 46,\;\mathrm{then}\;{r_{xy}}$, will be

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 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

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 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

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

The sum of absolute deviations about median is