Statistics practice · Mixed difficulty

The mean and variance of 7 observations are 8 and 16 respectively. If the observation are $2,4,10,12,14, x, y$, then value of $x y$ is

If $\bar{x}_1$ and $\sigma_1$ are the mean and standard deviation of the first distribution and $\bar{x}_2$ and $\sigma_2$ are the mean and standard deviation of the second distribution.

I. CV (1st distribution)$=\frac{\sigma_1}{\overline{{x}}_1} \times 100$

II. CV (2nd distribution)$=\frac{\overline{{x}}_2}{\sigma_2} \times 100$

III. For $\overline{{x}}_1=\overline{{x}}_2$, the series with lesser value of standard deviation is said to be more variable than the other.

IV. For $\overline{{x}}_1=\overline{{x}}_2$, the series with greater value of standard deviation is said to be more consistent than the other.

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

The AM of n observations is M. If the sum of n-4 observations is a, then the mean of remaining 4 observations is

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 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

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

For a group containing 100 observation, the mean and
standard deviation are 8 and $\sqrt{10.5}.$ For 50 observations selected from these 100 observations, the mean
and standard deviation are 10 and 2 respectively . The
standard deviation of the other half 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

If the variance of the frequency distribution is 160 , then the value of $c \in N$ is
$\boxed{\begin{array}{cccccccccccccccccccc} x&c&{2c}&{3c}&{4c}&{5c}&{6c} \\ f&2&1&1&1&1&1 \end{array}}$

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