JEE Statistics PYQs With Video Solutions, Download PDF

If the variance of the first $$n$$ natural numbers is 10 and the variance of the first $$m$$ even natural numbers is 16, then the value of $$m + n$$ is equal to

If the variance of the terms in an increasing A.P. $$b_1, b_2, b_3, \ldots, b_{11}$$ is 90 then the common difference of this A.P. is ___________.

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then $$\left(\frac{\text{mean of X}}{\text{standard deviation of X}}\right)$$ is equal to:

Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, x >  y, be 8 and 16 respectively. Two numbers are chosen from {1, 2, 3, x - 4,y,5} one after an other without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :

Consider a set of $$3n$$ numbers having variance 4. In this set, the mean of first $$2n$$ numbers is 6 and the mean of the remaining $$n$$ numbers is 3. A new set is constructed by adding 1 into each of the first $$2n$$ numbers, and subtracting 1 from each of the remaining $$n$$ numbers. If the variance of the new set is $$k$$, then $$9k$$ is equal to ________.

Consider a data consisting of 10 observations $$x_1,x_2,\dots,x_{10}$$, whose mean is $$5$$ and variance is $$7$$. If the mean and the variance of the first 8 observations $$x_1,x_2,\dots,x_8$$ are $$4$$ and $$3.5$$, respectively, and $$x_9 < x_{10}$$, then the value of $$3x_9 + 2x_{10}$$ is ___________.

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If $$\sigma$$ is the standard deviation of the data after omitting the two wrong observations from the data, then $$38\sigma^2$$ is equal to ______.

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:

Let $$x_1, x_2, x_3, \ldots, x_{20}$$ be in geometric progression with $$x_1 = 3$$ and the common ratio $$\frac{1}{2}$$. A new data is constructed replacing each $$x_i$$ by $$(x_i - i)^2$$. If $$\bar{x}$$ is the mean of new data, then the greatest integer less than or equal to $$\bar{x}$$ is

Let $$X = \{x \in N : 1 \le x \le 17\}$$ and $$Y = \{ax + b : x \in X \text{ and } a, b \in R, a > 0\}$$. If mean and variance of elements of Y are 17 and 216 respectively then $$a + b$$ is equal to:

A student scores the following marks in five tests: 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:

If the variance $$\sigma^2$$ of the data

is $$k$$, then the value of $$[k]$$ is ______ (where $$.$$ denotes the greatest integer function)

Consider the data on x taking the values $$0, 2, 4, 8, \ldots, 2^n$$ with frequencies $$^nC_0, ^nC_1, ^nC_2, \ldots, ^nC_n$$ respectively. If the mean of this data is $$\frac{728}{2^n}$$, then n is equal to_______.

If the mean and variance of the following data: 6, 10, 7, 13, $$a$$, 12, $$b$$, 12 are 9 and $$\frac{37}{4}$$ respectively, then $$(a - b)^2$$ is equal to:

Let in a series of $$2n$$ observations, half of them are equal to $$a$$ and remaining half are equal to $$-a$$. Also by adding a constant $$b$$ in each of these observations, the mean and standard deviation of new set become 5 and 20, respectively. Then the value of $$a^2 + b^2$$ is equal to :

Suppose a class has 7 students. The average marks of these students in the mathematics examination is 62, and their variance is 20. A student fails in the examination if he/she gets less than 50 marks, then in worst case, the number of students can fail is

The outcome of each of 30 items was observed; 10 items gave an outcome $$\frac{1}{2} - d$$ each, 10 items gave outcome $$\frac{1}{2}$$ each and the remaining 10 items gave outcome $$\frac{1}{2} + d$$ each. If the variance of this outcome data is $$\frac{4}{3}$$ then $$|d|$$ equals:

If the statistical variance of the first $$n$$ natural numbers is exactly equal to $$10$$, determine the value of $$n$$.

Let the Mean and Variance of five observations $$x_1 = 1, x_2 = 3, x_3 = a, x_4 = 7$$ and $$x_5 = b$$, $$a \gt b$$, be 5 and 10 respectively. Then the Variance of the observations $$n + x_n$$, $$n = 1, 2, \ldots, 5$$ is

The frequency distribution of the age of students in a class of 40 students is given below.

If the mean deviation about the median is 1.25, then $$4x + 5y$$ is equal to :

A random varaible X takes values 0,1,2,3 with probabilities $$\frac{2a+1}{30},\frac{8a-1}{30},\frac{4a+1}{30}$$, b respectively, where $$a,b \epsilon R$$. let $$\mu$$ and $$\sigma$$ respectively be the mean and standard deviation of X such that $$\sigma^{2}+\mu^{2}=2$$. Then $$\frac{a}{b}$$ is equal to :

The mean of 5 observations is 5 and their variance is 8. If three of the observations are 2, 4, and 6, and the remaining two observations are $$a$$ and $$b$$ with $$a > b$$, then the value of the product expression $$a \cdot b$$ is equal to

The mean of 5 observations is 5 and their variance is 8. If three of the observations are 2, 4, and 6, and the remaining two observations are $$a$$ and $$b$$ with $$a > b$$, then the exact integer value of the product expression $$a \cdot b$$ is equal to

The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 out of 6 observations are 2, 4, 5 and 7, then the remaining two observations are:

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

The mean deviation about the mean for the data

is equal to :

If the median and the range of four numbers $$\{x, y, 2x + y, x - y\}$$, where $$0 < y < x < 2y$$, are 10 and 28 respectively, then the mean of the numbers is :

Let the mean of 50 observations is 15 and the standard deviation is 2. However, one observation was wrongly recorded. The sum of the correct and incorrect observations is 70. If the mean of the correct set of observations is 16, then the variance of the correct set is equal to

If the mean of $$4, 7, 2, 8, 6$$ and $$a$$ is $$7$$, then the mean deviation from the median of these observations is