Statistics practice · Mixed difficulty

The mean weight of 9 items is 15. If one more item is added to the series, the mean becomes 16. The value of 10th item is

If the angle $\alpha$ between two forces of equal magnitude is reduced to $\alpha-\frac{\pi}{3}$, then the magnitude of their resultant becomes $\sqrt{3}$ times of the earlier one. The angle $\alpha$ is

The mean of the values $0,1,2,3, \ldots .n,\;$ with the corresponding weights $^n{C_0}{,^n}{C_1}, \ldots .,\;{\;^n}{C_n}$ respectively, is

The correlation coefficient 0.5 between $x$ and $y$ means

If $x$ and $y$ are two random variables with the same standard deviation and coefficient of correlation $r$, then the coefficient of correlation between $x$ and $x+y$ is

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

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 and that of the group of women is 21, then the percentage of men and women in the group is

The mean of observations is 4.4 and the variance is 8.24 . If three of the five observations are 1,2 and 6 , then find the other two observations.

For a set of 100 observations, taking assumed mean as 4 , the sum of the deviations is $-11 \mathrm{~cm}$, and the sum of the squares of these deviations is $275 \mathrm{~cm}^2$. The coefficient of variation is

The AM of the series $1,\;2,\;4,\;8,\;16,\;...,{2^n},$ is

Mean deviation of the series $a, a+d, a+2 d, a+2 n d$ from its mean is

If two lines of regression are$3\bar x - 2\bar y + 1 = 0\;and\;2\bar x - \bar y - 2 = 0$, then $(\bar x,\;\bar y)$ is

If both the regression lines intersect perpendicularly, then

The average weight of a class of 14 students is $42 \mathrm{~kg}$. If the teacher is included then average weight increases by $400 \mathrm{~g}$, then weight of teacher is

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

If the mean of $4,7,2,8,6$ and $a$ is 7 , then the mean deviation from the median of these observations is

If the regression coefficient of $X$ on $Y$ and $Y$ on $X$ are -0.4 and -0.9 respectively, then the correlation coefficient between ${X}$ and ${Y}$ is

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

Statement-1: The variance of first $n$ even natural numbers is $\frac{n^2-1}{4}$.

Statement-2 : The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2 n+1)}{6}$.

The quartile deviation of daily wages (in Rs.) of 7 persons given below is
$12,7,15,10,17,17,25$

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-

The mean and standard deviation of the marks of 20 students were found to be 40 and 15 respectively. Later, it was discovered that a score of 60 was wrongly read as 40 , then the correct variance will be

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

The average rate of (i) motion in the case of a person who rides the first mile at $10 \mathrm{~m} / \mathrm{h}$, the next mile at $8 \mathrm{~m} / \mathrm{h}$ and the third mile at $6 \mathrm{~m} / \mathrm{h}$ (ii) increase in population which is the first decade has increased $20 \%$ in the next $25 \%$ and in the third $44 \%$ are (where, $\log 20=1.3010$, $\log 25=1.3979, \log 28.02=1.4475$, $\log 44=1.6435$ )

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