Statistics and Probability

The variance of $5, 10, 15$ is:

Which measure of dispersion is calculated in the same units as the mean?

If $SD(x) = 3$, what is $SD(2x + 5)$?

The mean deviation about the median for $1, 2, 3, 4, 5$ is:

The mean and variance of five observations are $4.4$ and $8.24$, respectively. If three of the observations are $1$, $2$, and $6$, find the other two observations.

What is the mean deviation about the mean for $10, 20, 30, 40, 50, 60$?

Find the mean deviation about the median for the set: $1, 2, 3, 4, 5, 6$.

Find the variance of the set $\{x-1, x, x+1\}$.

If the mean deviation about the mean is $4$ for a set of $5$ observations, what is the sum of the absolute deviations from the mean?

The variance of $x_1, x_2, \dots, x_n$ is $\sigma^2$. The variance of $ax_1+b, ax_2+b, \dots, ax_n+b$ is:

If the standard deviation of a population is $8$, what is the variance?

Calculate the mean deviation about the mean for: $5, 5, 5, 5$.

The Coefficient of Variation is used to compare:

If the sum of squares of $n$ observations is $S$ and the mean is $M$, the variance formula is:

If the mean of $2, 4, 6, 8, 10$ is $\bar{x}$, then $\sum (x_i - \bar{x})^2$ is:

Variance of $10$ observations is $16$. If each observation is increased by $2$ and then multiplied by $3$, the new variance is:

The mean deviation about the mean for the data $4, 7, 8, 9, 10, 12, 13, 17$ is:

Two sets of data, each consisting of $10$ observations, have the same arithmetic mean. Their coefficients of variation are $12\%$ and $16\%$ respectively. If the standard deviation of the combined set of $20$ observations is $5\sqrt{2}$, find the value of their common arithmetic mean.

Mean and standard deviation of $100$ observations were $20$ and $3$. Later it was found that three observations $21, 21, 21$ were incorrect and they were recorded as $18, 20, 22$. What is the correct mean?

If the standard deviation of $n$ observations is $k$, then the sum of squares of deviations of these observations from their mean is:

If $P(A) = 0.2, P(B) = 0.3, P(C) = 0.4$ and $A, B, C$ are mutually exclusive events, then $P(A \cup B \cup C)$ is:

The collection of all subsets of a sample space $S$ is called the:

If $P(A) = 0.7$, then $P(A \cap S)$ is:

If three coins are tossed, how many elements are in the sample space $S$?

If $P(A) = 0.3$ and $P(A \cup B) = 0.6$, and it is known that $A$ and $B$ are independent events, find $P(B)$.

If $P(A \cup B) = 0.8, P(A \cap B) = 0.2$, and $P(A^c) = 0.4$, find $P(B)$.

Given $P(A) = 0.7$ and $P(B) = 0.8$, what is the maximum possible value of $P(A^c \cup B^c)$?

Two numbers $a$ and $b$ are chosen from $\{1, 2, \dots, 10\}$ with replacement. What is the probability that the roots of $x^2 + ax + b = 0$ are real?

The letters of the word 'SOCIETY' are arranged in a row. What is the probability that the three vowels are together?

If $P(A) = 0.7, P(B) = 0.4$ and $P(A \cap B) = 0.3$, then $P(A^c \cap B^c)$ is equal to:

In the experiment of rolling a die, if $E = \{2, 4, 6\}$, then $E$ is a/an:

Which of these is the correct expression for $P(A \cap B')$?

If $P(A) = \frac{1}{3}$ and $P(B) = \frac{1}{4}$, and $A$ and $B$ are mutually exclusive, what is $P(A \cup B)$?

The probability of getting a number less than $7$ on a single roll of a standard die is:

Two coins are tossed. Find the probability of getting exactly one head.

A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is either a King or a Queen?

If the probability of an event $A$ is $2/5$ and that of event $B$ is $3/10$, find $P(A' \cap B')$ assuming $A$ and $B$ are mutually exclusive.

If $P(A) = 0.4$ and $P(A \cup B) = 0.7$, and $A, B$ are mutually exclusive, find $P(B')$.

The probability that a man hits a target is $1/4$. How many times must he shoot so that the probability of hitting at least once is greater than $2/3$?

In a certain test, the probability of passing is $0.3$. If 10 students take the test, what is the probability that at most 1 passes?

If $b_{yx}$ and $b_{xy}$ are both greater than zero, then $r$ must be:

If the covariance between $X$ and $Y$ is zero, then the variables are:

In the regression equation $Y = 10 - 1.5X$, the value of the slope is:

If the two regression lines are $Y = 2X + 1$ and $X = 0.125Y + 2$, find the correlation coefficient $r$.

If $r = 0$, the regression lines are parallel to:

Find the mean of $Y$ if the regression line of $Y$ on $X$ is $2y - 3x + 4 = 0$ and $\bar{x} = 4$.

If $b_{yx} = 4$ and $b_{xy} = 1/9$, the correlation coefficient is:

For two variables $x$ and $y$, the equations of regression lines are $x + 2y - 5 = 0$ and $2x + 3y - 8 = 0$. Find the ratio of the variance of $x$ to the variance of $y$.

If $n=5$, $\sum d^2 = 20$, and there are two ties of two observations each (two groups of two), calculate the corrected Spearman's rank correlation coefficient.

In a bivariate data, $b_{yx} = 0.85$ and $b_{xy} = 0.85$. The angle between the regression lines is $\tan^{-1}(m)$. Find $m$ in terms of $r$.