Statistics PYQs - Last 10 Years

JEE Main / Mathematics / Algebra / 129 recent questions

MathematicsAlgebra2017-2026

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Practice 129 JEE Main Mathematics questions from Statistics. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

129

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

74

Last 5 Years

2022-2026

129

Last 10 Years

2017-2026

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202122 max PYQs/year2026

Question Types

129PYQs

MCQ70.5%

INTEGER29.5%

Difficulty Mix

#1 Medium100

#2 Easy25

#3 Hard4

74 in last 5 years129 in last 10 years

Last 10 Years Statistics Questions

Showing 50 of 129 filtered questions.

Let the six numbers \(\mathrm{a_1,a_2,a_3,a_4,a_5,a_6}\), be in A.P. and \(\mathrm{a_1+a_3=10}\). If the mean of these six numbers is \(\frac{19}{2}\) and their variance is \(\sigma^2\), then 8\(\sigma^2\) is equal to :

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :

Let \(9=x_{1} < x_{2} < \ldots < x_{7}\) be in an A.P. with common difference d. If the standard deviation of \(x_{1}, x_{2}..., x_{7}\) is 4 and the mean is \(\bar{x}\), then \(\bar{x}+x_{6}\) is equal to :

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is :

Let the mean of the data

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INTEGER+4 / -12023

The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is _________

INTEGER+4 / -12023

Let the positive numbers \(a_{1}, a_{2}, a_{3}, a_{4}\) and \(a_{5}\) be in a G.P. Let their mean and variance be \(\frac{31}{10}\) and \(\frac{m}{n}\) respectively, where \(m\) and \(n\) are co-prime. If the mean of their reciprocals is $$...

INTEGER+4 / -12023

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 fr...

Let the mean of 6 observations \(1,2,4,5, \mathrm{x}\) and \(\mathrm{y}\) be 5 and their variance be 10 .

Then their mean deviation about the mean is equal to :

If the mean of the frequency distribution

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INTEGER+4 / -12023

Let \(\mu\) be the mean and \(\sigma\) be the standard deviation of the distribution

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Let the mean and the variance of 5 observations x1, x2, x3, x4, x5 be \({24 \over 5}\) and \({194 \over 25}\) respectively. If the mean and variance of the first 4 observation are \({7 \over 2}\) and a respectively, then (4a + x5) is equal ...

The number of values of a \(\in\) N such that the variance of 3, 7, 12, a, 43 \(-\) a is a natural number is :

Let the mean and the variance of 20 observations \(x_{1}, x_{2}, \ldots, x_{20}\) be 15 and 9 , respectively. For \(\alpha \in \mathbf{R}\), if the mean of $$\left(x_{1}+\alpha\right)^{2},\left(x_{2}+\alpha\right)^{2}, \ldots,\left(x_{20}+\...

INTEGER+4 / -12022

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.

INTEGER+4 / -12022

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 stud...

INTEGER+4 / -12022

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 \(\left(x_{i}-i\right)^{2}\). If \(\bar{x}\) is the mean of...

INTEGER+4 / -12022

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and \({9 \over 4}\) respectively. Then \({x^4} + {y^2}\) is equal to :

The mean and variance of 10 observations were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is _____________.

INTEGER+4 / -12022

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 :

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct v...

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 ob...

INTEGER+4 / -12022

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is \({{5(n + 1)} \over n}\), then n is equal to ______________.

INTEGER+4 / -12022

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :

The mean of 10 numbers 7 \(\times\) 8, 10 \(\times\) 10, 13 \(\times\) 12, 16 \(\times\) 14, ....... is ____________.

INTEGER+4 / -12021

The mean and variance of 7 observations are 8 and 16 respectively. If two observations are 6 and 8, then the variance of the remaining 5 observations is :

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

Let the mean and variance of the frequency distribution\(\matrix{ {x:} & {{x_1} = 2} & {{x_2} = 6} & {{x_3} = 8} & {{x_4} = 9} \cr {f:} & 4 & 4 & \alpha & \beta \cr }\)be 6 and 6.8 respectively. If x3 is changed from 8 to 7, ...

Let n be an odd natural number such that the variance of 1, 2, 3, 4, ......, n is 14. Then n is equal to _____________.

INTEGER+4 / -12021

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If $$\mu$...

INTEGER+4 / -12021

Let X1, X2, ......., X18 be eighteen observations such that \(\sum\limits_{i = 1}^{18} {({X_i} - } \alpha ) = 36\) and \(\sum\limits_{i = 1}^{18} {({X_i} - } \beta {)^2} = 90\), where \(\alpha\) and \(\beta\) are distinct real numbers. If t...

INTEGER+4 / -12021

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. if \(\alpha\) and \(\sqrt \beta\) are the mean and standard deviatio...

Let the mean and variance of four numbers 3, 7, x and y(x > y) be 5 and 10 respectively. Then the mean of four numbers 3 + 2x, 7 + 2y, x + y and x \(-\) y is ______________.

INTEGER+4 / -12021

Consider the following frequency distribution :
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INTEGER+4 / -12021

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation \(\sqrt {13.44}\), then the standard deviation of the second sample is :

If the variance of 10 natural numbers 1, 1, 1, ....., 1, k is less than 10, then the maximum possible value of k is ________.

INTEGER+4 / -12021

Consider the following frequency distribution :
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INTEGER+4 / -12021

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 :

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and \({{20} \over 3}\), respectively, then the value of | a \(-\) b | is equal to :

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly ...

INTEGER+4 / -12021

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. The...

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 first 2n numbers, and subtracting 1 from each of ...

INTEGER+4 / -12021

Consider three observations a, b, and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?

Consider the statistics of two sets of observations as follows :

Size
Mean
Variance

Observation I
10
2
2

Observation II
n
3
1

If the variance of the combined set of thes...

INTEGER+4 / -12021

Let the observations xi (1 \(\le\) i \(\le\) 10) satisfy the
equations, \(\sum\limits_{i = 1}^{10} {\left( {{x_1} - 5} \right)}\) = 10 and \(\sum\limits_{i = 1}^{10} {{{\left( {{x_1} - 5} \right)}^2}}\) = 40.
If \(\mu\) and $$\lambda...

The mean and the standard deviation (s.d.) of
10 observations are 20 and 2 resepectively.
Each of these 10 observations is multiplied by
p and then reduced by q, where p \(\ne\) 0 and
q \(\ne\) 0. If the new mean and new s.d. become
hal...

The mean and variance of 20 observations are
found to be 10 and 4, respectively. On
rechecking, it was found that an observation 9
was incorrect and the correct observation was
11. Then the correct variance is

If the variance of the first n natural numbers is 10 and the variance of the first m even natural
numbers is 16, then m + n is equal to_____.

INTEGER+4 / -02020

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively,
then x.y is equal to _______.

INTEGER+4 / -02020

If \(\sum\limits_{i = 1}^n {\left( {{x_i} - a} \right)} = n\) and \(\sum\limits_{i = 1}^n {{{\left( {{x_i} - a} \right)}^2}} = na\)
(n, a > 1) then the standard deviation of n
observations x1
, x2
, ..., xn
is :