Statistics practice · Mixed difficulty

In a bivariate data $\mathrm{\Sigma }x = 30,\;\mathrm{\Sigma }y = 400,\;\mathrm{\Sigma }{x^2} = 196,\;\mathrm{\Sigma }xy = 850\;and\;n = 10.\;$. the regression coefficient of y on x is

The average of the four-digit numbers that can be formed using each of the digits 3, 5, 7 and 9 exactly once in each number, is

If $\operatorname{Cov}(x, y)=-165, \operatorname{Var}(x)=2.89, \operatorname{Var}(y)=100$, then the coefficient of correlation is

The mean life of a sample of 60 bulbs was $650 \mathrm{~h}$ and the standard deviation was 8h. A second sample of 80 bulbs has a mean life of $660 \mathrm{~h}$ and standard deviation $7 \mathrm{~h}$. Find the overall standard deviation.

Mode of the data $5,7,2,7,7,4,7,7,6,7$ is

If a variable $x$ takes values ${x_i}$ such that $a \le {x_i} \le b$, for $i = 1,\;2,\; \ldots n$, then

If $25 \%$ of the items are less than $20$ and $25 \%$ are more then $40$ , the quartile deviation is

10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of the combined set is given by

Consider the following data
$1,2,3,4,5,6,7,8,9,10$
If 1 is added to each number, then variance of the numbers so obtained is

The median value of observations $83,54,78,64,90$, $59,67,72,70,73$ is

For the given data, the calculation corresponding to all values of variates $\left( {x,y} \right)$ is following $\;\sum {\left( {x - \bar x} \right)^2} = 36,\;\sum {\left( {y - \bar y} \right)^2} = 25,\;\sum \left( {x - \bar x} \right)\left( {y - \bar y} \right) = 20$. The Karl Pearson’s correlation coefficient is

The weighted AM of first n natural numbers whose weights are equal to the corresponding numbers is equal to

Assuming the variance of four numbers $a , b, c$ and $d$ as 9, the variance of $5 a, 5 b, 5 c$ and $5 d$ is

The mean height of 15 students is $154 \mathrm{~cm}$. It is discovered later on that while calculating the mean the reading $175 \mathrm{cm}$. was wrongly read as $145 \mathrm{~cm}$. The correct mean height is

The arithmetic mean of the series ${ }^n C_0,{ }^n C_1,{ }^n C_2, \ldots$, ${ }^n C_n$ is

Let $\bar{x}, M$ and $\sigma^2$ be respectively the mean, mode and variance of $n$ observations $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{\mathrm{n}}$ and $\mathrm{d}_{\mathrm{i}}=-\mathrm{x}_{\mathrm{i}}-\mathrm{a}$, $\mathrm{i}=1,2, \ldots, \mathrm{n}$, where $\mathrm{a}$ is any number.

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

Statement II: Mean and mode of $\mathrm{d}_1, \mathrm{~d}_2, \ldots \mathrm{d}_{\mathrm{n}}$ are $-\overline{\mathrm{x}}-\mathrm{a}$ and $-\mathrm{M}-\mathrm{a}$, respectively.

The two lines of regression are given by $3x + 2y = 26\;and\;6x + y = 31.$ The coefficient of correlation between $x\;and\;y$ is

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If $\alpha$ and $\beta$ are the mean and standard deviation respectively for correct data, then $\left( {\alpha ,\,\beta } \right)$ is

A group of 10 items has arithmetic mean 6. If the arithmetic mean of 4 of these items is 7.5, then the mean of the remaining items is

One set containing five members has mean 8 , variance 18 and the second set containing three members has mean 8 and variance 24 . The variance of combined set of numbers is

Let ${x_i}(1 \le \,i\, \le \,10)$ be ten observations of a random variable $X.\,\mathrm{If}\,\sum\limits_{i = i}^{10} {({x_i} - p)} \, = \,3\,\mathrm{and}\,\sum\limits_{i = i}^{10} {{{({x_i} - p)}^2}\, = \,9\,\,}$ $p$ where $\mathrm{0} \ne \,p \in R,$ then the standard deviation of these observation is

For the arithmetic progression $a,\left( {a + d} \right),\left( {a + 2d} \right),\left( {a + 3d} \right), \ldots \ldots ,\left( {a + 2nd} \right)$, the mean deviation from mean is

Angle between two lines of regression is

If the regression coefficients are 0.8 and 0.2, then the value of coefficient of correlation is

Let $S$ be the set of all values of $a_1$ for which the mean deviation about the mean of 100 consecutive positive integers ${a_1},{a_2},{a_3},.....,{a_{100}}$ is 25. Then $S$ is

Statement-I: The series having greater CV is said to be
less variable than the other.

Statement-II: The series having lesser CV is said to be
more consistent than the other.

The variates $x$ and $u$ are related by $h u=x-a$, then correct relation between $\sigma_x$ and $\sigma_{\mathrm{a}}$ is

The correlation between $x$ and $a-x$ is

If the standard deviation of ${x_1},{x_2}, \ldots x$ is 3.5, then the standard deviation of $- 2{x_1} - 3,\; - 2{x_2} - 3,\; \ldots , - 2{x_n} - 3$ is

For a given distribution of marks, mean is 35.16 and its standard deviation is 19.76 . The coefficient of variation is