Statistics practice · Easy

The standard deviations of two sets containing 10 and 20 members are 2 and 3 , respectively measured from their common mean 5 . The SD for the whole set of 30 members is

The variance of 15 observations was found to be 8 . If each observation is multiplied by 4 , the new variance of the series is

In a class of 50 students, 10 have failed and their average marks are 28. The total marks obtained by the entire class are 2800. The average marks of those who have passed, are

If the sum of 11 consecutive natural numbers is 2761, then the middle number is

If $n=10, \bar{x}=12$ and $\Sigma x^2=1530$, then coefficient of variation is

The standard deviation of the wages of 85 employees is ₹ 15.40. After one year, each of them is given an increment of ₹ 25 . The standard deviation of new wages (in $\bar{₹}$ ) is

The mean deviation from the mean of the series $\mathrm{a},\mathrm{\;}a + d,a + 2\;d, \ldots ,a + 2nd,$ is

Harmonic mean of $2,4,5$ is.....

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

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

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

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

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

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

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

The mean deviation of any series is 15 , then the value of quartile deviation is