Statistics practice · Easy

When a particle be kept at rest under the action of the following forces

The correlation coefficient of two variable $x$ and $y$ is 0.8. The regression coefficient of $y$ on $x$ is 0.2, than the regression coefficient of $x$ on $y$ is

Let $\sigma$ be standard deviation of $n$ observations. Each observation is multiplied by a constant $c$. The standard deviation of resulting numbers is

If the heights of 5 persons are $144 \mathrm{~cm}, 153 \mathrm{~cm}, 150 \mathrm{~cm}, 158 \mathrm{~cm}$ and $155 \mathrm{~cm}$ respectively, then mean height is-

In an experiment with 15 observations onx, the following results were available $\sum {x^2} = 2830,\;\sum x = 170$. One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance is

If the first item is increased by 1, second by 2 and so on, then the new mean is

The quartile deviation of daily wages of 7 persons which are Rs. 12,7,15,10,17,17,25 is

Coefficient of variance of a distribution is $60 \%$ and the standard deviation is 25 . The arithmetic mean of the distribution is

If the frequencies of first four numbers out of $1,2,4,6,8$ are 2 , $3,3,2$, respectively, then the frequency of 8 , if their AM is 5 , is

The mean marks of 120 students is 20. It was later
discovered that two marks were wrongly taken as 50
and 80 instead of 15 and 18. The correct mean of
marks is

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $p$ and then reduced by $q,$ where $p \ne 0$ and $q \ne 0.$ If the new mean and new s.d. become half of their original values, then $q$ is equal to

The mean age of a combined group of men and women is 25 yr. If the mean age of the group of men is 26 yr and that of the group of women is 21 yr, then the percentage of men and women in the group are respectively

The mean of 6 distinct observation is 6.5 and their variance is 10.25. if 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are

The median of the following items $25,15,23,40,27,25,23,25$ and 20 is

The S.D. of the series $\mathrm{a},\mathrm{\;}a + d,a + 2\;d, \ldots ,a + 2nd,$ is

The geometric mean of the series $1,2,4, \ldots, 2^*$, is

The average of the squares of the numbers $0,\;1,\;2,\;3,4,\;...,\;n,$ is

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to:

If $25 \%$ of items are less than 10 and $25 \%$ are more than 40 , then coefficient of quartile deviation is

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is

The two lines of regression are $x+2 y-5=0$ and $x+3 y-8=0$. The coefficient of correlation between $x$ and $y$ is

The standard deviation of n observations ${x_1},{x_2}, \ldots ..,{x_n}\;$ is 2. If $\;\sum \limits_{i = 1}^n {x_i} = 20\;and\;\sum \limits_{i = 1}^n x_i^2 = 100$, then n is

The mean of 18 observations is 7 and if in each observation 5 is added, then the new mean will be

The median of 19 observations of a group is 30. If two observations with values 8 and 32 are further included, then the median of the new group of 21 observations will be

The mode of a set of observations $7,12,8,5,6,4,9$, $10,8,9,7,9,6,5,9$ is

The standard deviation of the numbers 31, 32, 33,…., 46, 47 is

For a series, the value of mean deviation is 15 . The most likely value of its quartile deviation is

The two lines of regression are $8 x-10 y=66$ and $40 x-18 y=214$ and variance of $x$ is 9 . The standard deviation of $y$ series is

Combined mean of two series $x_1$ and $x_2$, when $\Sigma x_1=210, \Sigma x_2=150, n_1=50, n_2=100$ is

The arithmetic mean of first $n$ odd natural numbers is