Statistics practice · Medium

If the s.d. of $n$ observations $x_1, x_2, \ldots, x_n$ is 4 and another set of $n$ observations $y_1, y_2, \ldots, y_n$ is 3, the s.d. of $n$ observations $x_1-y_1, x_2-y_2, \ldots, x_n-y_n$ is

A sample of 90 values has mean 55 and standard
deviation 3. A second sample of 110 values has mean
60 and standard deviation 2. The combined variance
is equal to (upto two decimal)

If for a distribution $\sum(x-5)=3, \sum(x-5)^2=43$ and the total number of items is 18.

Statement-I: Mean of the distribution is 4.1666.

Statement-II: Standard deviation of the distribution is 1.54.

Coefficient of variation of two distributions are $50 \%$ and $60 \%$ and their arithmetic means are 30 and 25 respectively. Difference of standard deviation is:

The ${7^{th}}$ percentile is equal to

Coefficient of variation of two distributions are 60% and 75%, and their standard deviation are 18 and 15
respectively, then their arithmetic means respectively are

If $\bar{x}$ is the mean and $\sigma^2$ is the variance of $n$ observations $x_1, x_2, \ldots, x_n$, then which of the following are true for the observations ${ax}_1, {ax}_2,{ax}_3, \ldots, {ax}_n?$

I. Mean of the observations is $\frac{\bar{x}}{{a}}$.

II. Variance of the observations is $\frac{\sigma^2}{{a}^2}$.

III. Mean of the observations is $a \bar{x}$.

IV. Variance of the observations is $a^2 \sigma^2$.

If the s.d. of a set of observations is 4 and if each observation is divided by 4, the s.d. of the new set of observations will be

The mean and the standard deviation (s.d.) of five observations are 9 and 0 , respectively.
If one of the observations is changed such that the mean of the new set of five observations becomes 10 , then their d. is?

If the variance of 1,2,3,4,5,…,10 is $\frac{{99}}{{12}}$, then the standard derivation of 3,6,9,12,…., 30 is

Three forces $P, Q, R$ are acting at a point in a plane. The angle between $P, Q$ and $Q, R$ are $150^{\circ}$ and $120^{\circ}$ respectively, then for equilibrium; forces $P, Q, R$ are in the ratio

A batsman scores sums in 10 innings 38, 70, 48, 34, 42, 55, 46, 63, 54 and 44, then the deviation from median is

A particle is acted upon by three forces $P, Q$ and $R$. It cannot be in equilibrium, if $P: Q: R=$

An aeroplane flies around a square, the sides of which measure 100 miles each. The aeroplane covers at a speed of $100 \mathrm{~m} / \mathrm{h}$ the first side, at $200 \mathrm{~m} / \mathrm{h}$ the seoond side, at $300 \mathrm{~m} / \mathrm{h}$ the third side and $400 \mathrm{~m} / \mathrm{h}$ the fourth side. The average speed of acroplane around the square is

The mean weight of $120$ students in the second year class of a college is $56 {~kg}$. If the mean weights of the boys and that of the girls in the class are $60 {~kg}$ and $50 {~kg}$ respectively, then the number of boys and girls separately in the class are

The mean of a data set consisting of 20 observations is 40 . If one observation 53 was wrongly recorded as 33 , then the correct mean will be:

Ravi obtained 70 and 75 marks in first two unit tests. Then, the minimum marks he should get in the third test to have an average of at least 60 marks, are

The weighted mean of first $n$ natural numbers whose weights are equal to the squares of corresponding numbers is

The mean of 5 observations is 3 and variance is 2. If three of the five observations are 1, 3, 5 the other two are

The mean income of a group of workers is $X$ and that of another group is $Y$. If the number of workers in the second group is 10 times the number of workers in the first group, then mean income of combined group is

The mean of $1,2,6$, a, b is 4 and their variance is 5.2 then $(\mathrm{a}, \mathrm{b})$

If variance of $X, Y, X-Y$ are respectively $\sigma_x^2, \sigma_y^2, \sigma_{x-y}^2$, then the coefficient of correlation $r$ between two variables $X$ and $Y$ is given by

A.M. of $C_0, 2 C_1, 3 C_2, \ldots,(n+1) C_n$, where $(1+x)^n=C_0+C_1 x+$ $C_2 x^2+\cdots+C_n x^n$ is equal to

The arithmetic mean of $a, a+d, a+2 d, \ldots, a+2 n d$ is

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :

If each observation of a raw data whose variance is ${\sigma ^2}$ is multiplied by $h\;$, then the variance of the new set is

The image of the line $\frac{{x - 1}}{3} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - 5}}$ in the plane $2x - y + z + 3 = 0$ is the line

Let the mean and the variance of 6 observations $a, b, 68,44,48,60$ be 55 and 194 , respectively. If $a>b$, then $a+3 b$ is

The correlation between $x$ and $a-x$ is

The mean of five observations is 4 and their variance is 5.2. If three of them are 1,2 and 6 , then the other two are