Statistics practice · Easy

If regression coefficient of $y$ on $x$ is 2 , then the regression coefficient of $x$ on $y$ is

The mean weight per student in a group of seven students is
55 kg. If the individual weights of 6 students are 52, 58, 55,
53, 56 and 54; then weights of the seventh student is

The standard deviation for the set of numbers $1,4,5$, 7,8 is 2.45 nearly. If 10 is added to each number, then new standard deviation is

The means and variance of n observations ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ are 5 and 0 respectively. If $\sum \limits_{i = 1}^n x_i^2 = 400$, then the value of n is equal to

A class of 30 boys and 15 girls is given a test in Mathematics. The average marks obtained by boys is 15 and by girls is 6 . The average of whole class is

Semi-interquartile range is

The mean of a set of number is $\bar{x}$ if each number is increased by $\lambda$, then mean of the new set is-

5 students of a class have an average height 150 cm and variance $18\mathrm{ }c{m^2}.$ A new student, whose height is 156 cm, joined them. The variance (in $c{m^2}$ )of the height of these six students is

A student scores the following marks in five tests 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

If the S.D. of a variable $X$ is $\sigma$, then the S.D. of $\frac{{a\;X + b}}{c}\left( {a,b,c\;\mathrm{are\;constant}} \right),$ is

If the standard deviation of numbers 2, 4, 5 and 6 is a constant $\alpha$, then the standard deviation of the numbers 4, 6, 7 and 8 is

The geometric mean of observations $2,4,16$ and 32 is

Suppose a population $A$ has 100 observations 101,102,….,200 and another population B has 100 observations 151,152,….,250 if ${V_A}\;and\;{V_B}$ represent the variances of the two populations respectively, then ${V_A}\;/\;{V_B}$ is

The correlation coefficient between $x\;and\;y$ from the following data $\sum x = 40,\;$ $\sum y = 50,\;\sum xy = 220,\;\sum {x^2} = 200,\;\sum {y^2} = 262,\;n = 10$ is

If $x$ and $y$ are deviations from arithmetic mean, $r=0.8$  $\Sigma x y=60, \sigma_y=2.5$ and $\Sigma x^2=90$, then the number of items in the series, is

The number of observations in a group is 40 . If the average of first 10 is 4.5 and that of the remaining 30 is 3.5 , then the average of the whole group is

The regression coefficient of $y$ on $x$ is $\frac{2}{3}$ and $x$ on $y$ is $\frac{4}{3}$. If the acute angle between the regression line is $\theta$, then $\tan \theta$ is equal to

If a variable takes values $0,1,2,3 \ldots$ with frequencies proportional to $e^{-\lambda}, e^{-\lambda} \lambda, \frac{e^{-\lambda} \lambda^2}{2 !}, \frac{e^{-\lambda} \lambda^3}{3 !}, \ldots$ then the mean of the distribution is

If the two lines of regression are $4x + 3y + 7 = 0\;\;and\;3x + 4y + 8 = 0,$ then the means of $x\;and\;y$ are

The mean of series $1,2,4,8, \ldots ., 2^n$ is

The number of children in 25 families of a locality are recorded as follows:
$3,1,4,0,2,1,1,2,3,3,2,2,2,5,0,1,4,1,2,1,2,3,0,1,4$
Then, mean number of children per family is

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

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 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 both the regression lines intersect perpendicularly, then