Statistics practice · Mixed difficulty

The best average of dealing a qualitative data is

If $\sigma$ is the standard deviation of a random variable $x$, then the standard deviation of the random variable $ax + b$, where$a,b \in R$ is

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

A uniform rod of weight $W$ and length $2 l$ is resting in a smooth spherical bowl of radius $r$. The rod is inclined to the horizontal at an angle of

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 the mean deviation of number $1,1 + d,1 + 2d, \ldots ..,1 + 100d$ from their mean is 255, then the d is equal to

Consider any set of observations $x_1, x_2, x_3, \ldots, x_{101}$; it being given that $x_1 < x_2 < x_3 < \ldots < x_{100} < x_{101}$, then the mean deviation of this set of observations about a point $k$ is minimum, when $k$ equals

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

If ${\bar x}$ is the arithmetic mean of n independent variates ${x_1},{x_2},{x_3}, \ldots ,{x_n}$ each of the standard derivation σ, then variance $\left( {\bar x} \right)$ 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

If $\bar{x}_1$ and $\bar{x}_2$ are means of two distribution such that $\bar{x}_1 < \bar{x}_2$ and $\bar{x}$ is the mean of the joint distribution, then

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

The greatest and least magnitude of the resultant of two forces of constant magnitude are $F$ and $G$. When the forces act an angle $2 \alpha$, the resultant in magnitudes is equal to

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

Mean and variance of 10 positive observations is 7 and 8. If we add 5 to each number then sum of mean
and variance of new data is