Statistics practice · Mixed difficulty

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.

Which of the following is correct about the series $24,38,55,69,89$ ?

Karl Pearson's coefficient of skewness of a distribution is 0.32 . Its $S D$ is 6.5 and mean 39.6. Then, the median of the distribution is given by

The variance of first 50 even natural numbers is

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 intersecting point of two regression lines 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 $a^2 \sigma^2$.

The AM of the series $1,2,4,8,16, \ldots ,{2^n},$ is

The mode of a moderately symmetrical series is 18 and mean is 24 . The median is

The mean of a set of 30 observations is 75 . If each other observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by 25 , their mean remains the same. The $\lambda$ is equal to

The coefficient of variation of two series are 70 and 90 and their standard deviation are 17.5 and 18 , respectively. The mean of two series are

The mean of the numbers $a,\,\,b,\,\,8,\,\,5,\,\,10$ is 6 and their variance is 6.8. If $M$ is the mean deviation of the numbers about the mean, then $25 M$ is equal to:

If the two regression coefficients are 0.8 and 0.2 , then the coefficient of correlation is

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?

Mean of 100 observation is 45. If it was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The correct mean 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 $P: Q: R=$

If mode of a data is 27 and mean is 24 , then median is

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

Quartile deviation is nearly equal to

In a moderately skewed distribution, the values of mean and median are 5 and 6 , respectively. The value of mode for such distribution 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:

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