Statistics practice · Mixed difficulty

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

Mean of 5 observations is 7 . If four of these observations are $6,7,8,10$ and one is missing then the variance of all the five observations is :

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 mean deviation about the median of the series of batsman in ten innings $34,38,42,44,46,48,54,55,56,76$ 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

If the standard deviation of 10 observations $x_1, x_2, \ldots . ., x_{10}$ is 4 and that of another set of 10 observations $y_1, y_2, \ldots \ldots y_{10}$ is 3 and also $X_i=\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right) . \bar{x}$ is mean of all $x_i$ 's and $\bar{y}$ is mean all $y_i$ 's and $\sum\limits_{{i=1}}^{10} X_i=80$. Then standard deviation of observations $x_1-y_1, x_2-y_2, \ldots \ldots, x_{10}-y_{10}$ 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 mean deviation from mean of observations $a, a+d, a+2 d, \ldots . ., a+2 n d$ 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 centre of mass of a rod of length ' $a$ ' $\mathrm{cm}$ whose density varies as the square of the distance from one end, will be at a distance

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

A data consists of $\mathrm{n}$ observations:

$x_1, x_2, \ldots, x_{\mathrm{n}} \text {. If } \sum_{i=1}^{\mathrm{n}}\left(x_i+1\right)^2=9 \mathrm{n} \text { and } \sum_{i=1}^{\mathrm{n}}\left(x_i-1\right)^2=5 \mathrm{n}$

then the standard deviation of this data 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

The mean of discrete observations ${y}_1, {y}_2, {y}_3, \ldots, {y}_{{n}}$ is given by

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

If $\sum \limits_{i = 1}^{18} \left( {{x_i} - 8} \right) = 9\;and\;\sum \limits_{i = 1}^{18} {\left( {{x_i} - 8} \right)^2} = 45$, then the standard derivation of ${x_1},{x_2}, \ldots ,{x_{18}}$ is

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is $₹ 54$ and per day mean wage of all the workers is $₹ 60$, then per day mean wage of the night shift workers (in $₹$ ) is :

The mean of 100 items is 50 and their S.D. is 4 . the sum of all the items and also the sum of the squares of the items is