Statistics practice · Medium

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

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

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

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

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

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
$12,7,15,10,17,17,25$

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

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, $\log 20=1.3010$, $\log 25=1.3979, \log 28.02=1.4475$, $\log 44=1.6435$ )

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

The mean deviation from mean of observations $a, a+d, a+2 d, \ldots . ., a+2 n d$ 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 mean of discrete observations ${y}_1, {y}_2, {y}_3, \ldots, {y}_{{n}}$ is given by

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 :

A car owner buys petrol at Rs. 7.50 , Rs. 8.00 and Rs. 8.50 per litre for 3 successive years. If he spends Rs. 4000 each year, then the average cost per litre of petrol is

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

If the standard deviation of the numbers 2, 3, $a$ and 11 is 3.5, then which of the following is true?

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of
the set is increased by 2, then the median of the new set

If $z=a x+b y$ and $r$ is the correlation coefficient between $x$ and $y$, then $\sigma_z^2$ is equal to