Statistics practice · Mixed difficulty

The mean and standard deviation of $1,2,3,4,5,6$ are

If the data ${x_1},{x_2},...,{x_{10}}$ is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of these is 2000, then the standard deviation of this data is

A motor car when travelling from rest travels the first twentieth of a mile at $6 \mathrm{~m} / \mathrm{h}$ the next three twentieths of the mile at $8,12,24 \mathrm{~m} / \mathrm{h}$ respectively. But its average speed over the first one-fifth of a mile is not $12.5 \mathrm{~m} / \mathrm{h}$, then the correct average is

The mean of 5 observations is 5 and their variance is 124.
If three of the observations are 1, 2 and 6; then the mean
deviation from the mean of the data is :

A man motors from $A$ to $B$. In motoring a distance uphill he gets a mileage of only 10 miles per gallon of gasoline. On the return trip, he makes 15 miles per gallon, then the harmonic mean of his mileage (verify that this is the proper average to be used, here assuming that the distance from $A$ to $B$ is 60 miles) is

The mean annual salaries paid to 1000 employees of a company was Rs. 3400 . The mean annual salaries paid to male and female employees were Rs. 200 and Rs. 4200, respectively. The percentage of males and females employed by the company are

In a moderately skewed distribution the values of mean and median are 5 and 6 respectively. The value of mode in such a situation is approximately equal to

If $b_{y x}$ and $b_{x y}$ are the regression coefficient of $y$ on $x$ and $x$ on $y$ respectively, then

Let $x_1, x_2, \ldots, x_{100}$ be in an arithmetic progression, with $x_1=2$ and their mean equal to 200 . If $y_i=i\left(x_i-i\right), 1 \leq i \leq 100$, then the mean of $y_1, y_2, \ldots$, $y_{100}$ is

The variance of $6,8,10,12,14$ is

If the mean of the data $7,7,9,7,8,7, \lambda, 8$ is 7, then the variance of this data is:

1, 2, 4, 6, 8, 9 transformed into another series whose mean is 12. Two middle terms of the transformed series are

The SD of 15 items is 6 and if each item is decreases by 1 , then standard deviation will be

The AM of n numbers of a series is ${\bar X}$. If the sum of first $(n\; - 1)$ terms is $k$ then the $n{\;^{th}}$ number is

In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is

If $\;\;\;{x_1},{x_2}, \ldots .,{x_{18}}$ 18 are observation such that $\sum \limits_{j = 1}^{18} \left( {{x_j} - 8} \right) = 9\;\;\;\;and\,\;\;\;\sum \limits_{j = 1}^{18} {\left( {{x_j} - 8} \right)^2} = 45,$ then these standard derivation of these observations is

Let $r>0$ and $m$ be the A. M. of the regression coefficient of $y$ on $x$ and $x$ on $y$, then

If $\sum\limits_{{i=1}}^5 x_i^2=40 \& \sum\limits_{{i=6}}^{10} x_j^2=20$ and mean of $x_1, x_2, \ldots \ldots x_5$, is 1 and mean of $x_6, x_7, \ldots \ldots . . . x_{10}$ is 2 then variance of $x_1, x_2, \ldots \ldots . . x_{10}$ is

The mean weight of 150 students in 60 Kgs. The
mean weight of boys is 70 and that of girls in 55
with standard deviations 10 and 15 respectively. The
combined variance is

The mean of 5 observation is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6, then difference of the other two observations is

If a variable X takes values $0,1,2, \ldots ,n$ with frequencies proportional to the binomial coefficients $^n{C_0},{\;^n}{C_1},{\;^n}{C_2}, \ldots ,{\;^n}{C_n},$ the mean square deviation about $x = 0,$ is

On thirteen consecutive days, the number of persons booked for violating speed limit of $40 \mathrm{~km} / \mathrm{h}$ were as follows:
$58,61,68,57,62,50,55,62,53,54,51,59,52$
The median number of speed violations per day is

The weighted mean of first $n$ natural number if their weight are the same as the number is-

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately

The mean deviation from mean of the observation $a,\;a + d,\;a + 2d,\; \ldots a + 2nd$ is

$n$ observations on a variable $X_i$ are $X_i=A+i B$ for $i=1,2,3 \ldots . n$ where $A, B$ are real constants. The mean of these observation is

If the mean of 15 observations is 12 and standard deviation is 3. If 12 is replaced by 10 (in data) then the new mean is $\mu$ and variance is $\sigma^2$ then what is the value of $15\left(\mu+\mu^2+\sigma^2\right)$

The first of two samples has 100 items with mean 15 and $SD = 3.$ If the whole group has 250 items with mean 15.6 and $SD = \sqrt {13.44}$, the SD of the second group is

In a college of 300 students every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers are

The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On respectively, it was found that an observation by mistake was taken 8 instead of 12. The correct standard deviation is