Statistics practice · Easy

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

Mean of $n$ items is $\bar{x}$. If these $n$ items are successively increased by $2,2^2, 2^3, \ldots, 2^n$, then the new mean is

If two regression lines are coincident, then which is correct?

A sample of 35 observations has the mean as 30 and SD as 4. A second sample of 65 observations from the same population has mean as 70 and SD as 3. The SD of the combined sample is

Let $X = \left\{ {x\varepsilon N:1 \le x \le 17} \right\}$ and $Y = \left\{ {ax + b:x \in X\,\mathrm{and}\,a,b \in R,a > 0} \right\}$ If mean and variance of elements of Y are 17 and 216 respectively, then a+b is equal to

If $\operatorname{Cov} .({X}, {Y})=-16.5, \operatorname{Var} .({X})=2.89$ and $\operatorname{Var} .({Y})=$ $100$ then coefficient of correlation $\rho(X, Y)$ is equal to

If the values $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \ldots, \frac{1}{n}$ occur at frequencies $1,2,3,4,5, \ldots, n$, in a distribution, then the mean is

If the arithmetic mean of 9 observations is 100 and that of 6 is 80 . Then, the combined mean of all the 15 observations will be

The variance of the data 2, 4, 6, 8, 10 is

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

The standard deviation of $-1,-2,-3,-4,-5,-6,-7$ is

If $\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right) = 9\mathrm{ }}$ and $\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2} = 45}$, then the standard deviation of the 9 items then the standard deviation of the 9 items ${x_1},{x_2},...,{x_9}$ is

If the correlation coefficient between $x$ and $y$ is 0.6 and if $u=\frac{{X}-5}{2}$ and $v=\frac{{Y}-3}{3}$ then the coefficient of correlation between $u$ and $v$ is

If the mean of numbers $27,31,89,107,156$ is 82 , then the mean of $130,126,68,50,1$ is

The mean wage of 1000 workers in a factory running in two shifts of 700 and 300 workers is Rs. 500 . The mean wage of 700 workers working in day shift is Rs. 450 . The mean wage of workers working in the night shift is

The test marks in Statistics for a class are 20, 24, 27, $38,18,42,35,21,44,18,31,36,41,26,29$. The median score of the class is

The coefficient of correlation $(r)$ and the two regression coefficients ${b_{yx}},\;{b_{xy}}$ are related as

Let the six numbers $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}$ be in A.P. and $a_{1}+a_{3}=10$. If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^{2}$, then $8 \sigma^{2}$ is equal to:

The mean of the squares of first $n$ natural numbers is

The arithmetic mean of the squares of the first $n$ natural numbers is

The means of a set of numbers is ${\bar X}$ . If each number is divided by 3, then the new mean is

Mean of 25 observations was found to be 78.4. But later on it was found that 96 was misread 69 . The correct mean is

For observation set $x$ data obtained is $x_i=\{11,12,13, \ldots 41\}$

For another observation set $y$ data obtained is $y_i=\{61,62,63, \ldots 91\}$

Then value of $\bar{x}+\bar{y}+\sigma^2$ where $\bar{x}, \bar{y}$ are means of respective data set while $\sigma^2$ is variance of combined data is

If the mean of n observation ${1^2},{2^2},{3^2}, \ldots .,{n^2}\;\;\mathrm{is}\;\;\frac{{46n}}{{11}}$, then n is equal to

If $\mu$ is the mean of a distribution, then $\sum f_i\left(y_i-\mu\right)$ is equal to

The best average of dealing a qualitative data is

If $\sigma$ is the standard deviation of a random variable $x$, then the standard deviation of the random variable $ax + b$, where$a,b \in R$ is