How many questions from Statistics appear in JEE?

Statistics has appeared in 118 of the last 186 JEE Main and JEE Advanced papers — about 63% of them — contributing 118 questions in total across those papers.

Is Statistics an important chapter for JEE?

Judged by how often it is actually tested, it appears in roughly 63% of papers. Chapters above about 50% are effectively guaranteed to show up every session, so they repay thorough preparation; lower-frequency chapters are better treated as targeted revision.

Where do these Statistics questions come from?

Every question is from an official JEE Main or JEE Advanced paper, transcribed from the original paper and tagged to this chapter. Answers follow the official answer key.

Statistics JEE Previous Year Questions with Answers

Q1·MathematicsNumericalJEE Advanced 2026

Consider a data consisting of 10 observations

x_{1}, x_{2}, \ldots, 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}, \ldots, x_{8}

are 4 and 3.5, respectively, and

x_{9} < x_{10}

, then the value of

3x_{9} + 2x_{10}

is _____.

Q2·MathematicsSingle correctJEE Main 2026

A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of all these 10 observations is equal to:

(A)5.96
(B)6.14
(C)6.04
(D)6.24

Q3·MathematicsSingle correctJEE Main 2026

Let the mean and the variance of seven observations 2, 4, α, 8, β, 12, 14, α < β, be 8 and 16 respectively. Then the quadratic equation whose roots are 3α + 2 and 2β + 1 is :

(A) $x^{2} - 35x + 306 = 0$
(B) $x^{2} - 41x + 420 = 0$
(C) $x^{2} - 45x + 506 = 0$
(D) $x^{2} - 37x + 342 = 0$

Q4·MathematicsSingle correctJEE Main 2026

A data consists of 20 observations x

_1

, x

_2

, ..., x

_{20}

. If

\sum_{i=1}^{20}(x_i + 5)^2 = 2500

and

\sum_{i=1}^{20}(x_i - 5)^2 = 100

, then the ratio of mean to standard deviation of this data is:

(A)2 : 1
(B)3 : 1
(C)3 : 2
(D)4 : 1

Q5·MathematicsSingle correctJEE Main 2026

The mean deviation about the mean for the data is equal to:

$x_i$	$f_i$
5	8
7	6
9	2
10	2
12	2
15	6

(A) $\frac{40}{13}$
(B) $\frac{42}{13}$
(C) $\frac{44}{13}$
(D) $\frac{46}{13}$

Q6·MathematicsSingle correctJEE Main 2026

A variable X takes values

0, 0, 2, 6, 12, 20, \ldots, n(n - 1)

with frequencies

^{n}C_0, ^{n}C_1, ^{n}C_2, ^{n}C_3, ^{n}C_4, ^{n}C_5, \ldots, ^{n}C_n

, respectively. If the mean of this data is 60, then its median is :

(A)56
(B)42
(C)72
(D)90

Q7·MathematicsSingle correctJEE Main 2026

For 10 observations

x_{1}, x_{2}, \ldots, x_{10}

, if

\sum_{i=1}^{10}(x_{i} + 2)^{2} = 180

and

\sum_{i=1}^{10}(x_{i} - 1)^{2} = 90

, then their standard deviation is:

(A)2
(B) $\sqrt{3}$
(C) $2\sqrt{2}$
(D)3

Q8·MathematicsSingle correctJEE Main 2026

Suppose that the mean and median of the non-negative numbers

21, 8, 17, a, 51, 103, b, 13, 67, (a > b)

, are 40 and 21, respectively. If the mean deviation about the median is 26, then

2a

is equal to:

(A) $109$
(B) $117$
(C) $161$
(D) $131$

Q9·MathematicsSingle correctJEE Main 2026

The mean and variance of

n

observations are 8 and 16, respectively. If the sum of the first

(n - 1)

observations is 48 and the sum of squares of the first

(n - 1)

observations is 496, then the value of

n

is:

(A) $21$
(B) $16$
(C) $13$
(D) $7$

Q10·MathematicsSingle correctJEE Main 2026

If the mean of the data is 21, then

k

is one of the roots of the equation :

Class	5 − 10	10 − 15	15 − 20	20 − 25	25 − 30	30 − 35
Frequency	2	$k$	28	54	$k+1$	5

(A) $2x^{2}-23x-10=0$
(B) $4x^{2}-35x+24=0$
(C) $2x^{2}-19x-10=0$
(D) $2x^{2}-35x+98=0$

Q11·MathematicsSingle correctJEE Main 2026

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2, 3, 5, 10, 11, 13, 15, 21, then the mean deviation about the median of all the 10 observations is

(A)5
(B)4
(C)6
(D)7

Q12·MathematicsSingle correctJEE Main 2026

Let

X = \{x \in \mathbb{N} : 1 \le x \le 19\}

and for some a, b

\in \mathbb{R}

,

Y = \{ax + b : x \in X\}

. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of b is

(A)20
(B)80
(C)100
(D)60

Q13·MathematicsSingle correctJEE Main 2026

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations α in this data is replaced by β, then the mean and variance become 10.1 and 1.99, respectively. Then α + β equals.

(A)10
(B)15
(C)5
(D)20

Q14·MathematicsSingle correctJEE Main 2026

Let the mean and variance of 8 numbers -10, -7, -1, x, y, 9, 2, 16 be

\frac{7}{2}

and

\frac{293}{4}

, respectively. Then the mean of 4 numbers x, y, x + y + 1, |x - y| is:

(A)11
(B)9
(C)10
(D)12

Q15·MathematicsSingle correctJEE Main 2026

If the mean and the variance of the data Class | 4–8 | 8–12 | 12–16 | 16–20 Frequency | 3 |

\lambda

| 4 | 7 are µ and 19 respectively, then the value of λ + µ is

(A)18
(B)21
(C)20
(D)19

Q16·MathematicsSingle correctJEE Main 2026

If the mean deviation about the median of the numbers k, 2k, 3k, ...., 1000k is 500, then

k^{2}

is equal to :

(A)16
(B)4
(C)1
(D)9

Q17·MathematicsSingle correctJEE Advanced 2025

Consider the following frequency distribution: Value | 4 | 5 | 8 | 9 | 6 | 12 | 11 Frequency | 5 |

f_1

|

f_2

| 2 | 1 | 1 | 3 Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For the given frequency distribution, let α denote the mean deviation about the mean, β denote the mean deviation about the median, and

\sigma^2

denote the variance. Match each entry in List-I to the correct entries in List-II. The correct option is:

List-I	List-II
P. $7f_1 + 9f_2$ is equal to	1.146
Q.19α is equal to	2.47
R.19β is equal to	3.48
S. $19\sigma^2$ is equal to	4.145
	5.55

(A)(P) → (5), (Q) → (3), (R) → (2), (S) → (4)
(B)(P) → (5), (Q) → (2), (R) → (3), (S) → (1)
(C)(P) → (5), (Q) → (3), (R) → (2), (S) → (1)
(D)(P) → (3), (Q) → (2), (R) → (5), (S) → (4)

Q18·MathematicsSingle correctJEE Main 2025

The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are

\mu

and

\sigma

respectively, then

10(\mu+\sigma)

is equal to

(A)445
(B)451
(C)447
(D)449

Q19·MathematicsSingle correctJEE Main 2025

Let the mean and the standard deviation of the observation

2, 3, 3, 4, 5, 7, a, b

be 4 and

\sqrt2

respectively. The mean deviation about the mode of these observations is:

(A)1
(B) $\dfrac{3}{4}$
(C)2
(D) $\dfrac{1}{2}$

Q20·MathematicsSingle correctJEE Main 2025

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>b

, be 5 and 10 respectively. Then the Variance of the observations

n+x_n

,

n=1,2,\ldots,5

is:

(A)17
(B)16.4
(C)17.4
(D)16

Q21·MathematicsSingle correctJEE Main 2025

If the mean and variance of

6, 4, a, 8, b, 12, 10, 13

are 9 and

\dfrac{37}{4}

respectively, then

a+b+ab

is equal to:

(A)105
(B)103
(C)100
(D)106

Q22·MathematicsSingle correctJEE Main 2025

Let

x_1, x_2,\ldots,x_{10}

be ten observations such that

\displaystyle\sum_{i=1}^{10}(x_i-2)=30

,

\displaystyle\sum_{i=1}^{10}(x_i-\beta)^2=98

,

\beta>2

and their variance is

\dfrac{4}{5}

. If

\mu

and

\sigma^2

are respectively the mean and the variance of

2(x_1-1)+4\beta,\ 2(x_2-1)+4\beta,\ \ldots,\ 2(x_{10}-1)+4\beta

, then

\dfrac{\beta\mu}{\sigma^2}

is equal to:

(A)100
(B)110
(C)120
(D)90

Q23·MathematicsSingle correctJEE Main 2025

For a statistical data

x_1,x_2,\ldots,x_{10}

of 10 values, a student obtained the mean as 5.5 and

\sum_{i=1}^{10}x_i^2=371

. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is

(A) $7$
(B) $4$
(C) $9$
(D) $5$

Q24·MathematicsSingle correctJEE Main 2025

Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is

(A) $48$
(B) $44$
(C) $40$
(D) $52$

Q25·MathematicsIntegerJEE Main 2025

The variance of the numbers

8,\ 21,\ 34,\ 47,\ \ldots,\ 320

, is __________.

Q26·MathematicsSingle correctJEE Main 2024

The frequency distribution of the age of students in a class of 40 students is given below. Age: 15, 16, 17, 18, 19, 20; No. of Students: 5, 8, 5, 12,

x

,

y

. If the mean deviation about the median is

1.25

, then

4x + 5y

is equal to :

(A)43
(B)44
(C)47
(D)46

Q27·MathematicsSingle correctJEE Main 2024

If the variance of the frequency distribution given by

x

:

c

,

2c

,

3c

,

4c

,

5c

,

6c

with corresponding frequencies

f

:

2

,

1

,

1

,

1

,

1

,

1

is 160, then the value of

c\in\mathbb{N}

is:

(A) $5$
(B) $8$
(C) $7$
(D) $6$

Q28·MathematicsNumericalJEE Main 2024

Let

a

,

b

,

c\in\mathbb{N}

and

a<b<c

. Let the mean, the mean deviation about the mean and the variance of the 5 observations

9

,

25

,

a

,

b

,

c

be

18

,

4

and

\dfrac{136}{5}

, respectively. Then

2a+b-c

is equal to _______ .

Q29·MathematicsSingle correctJEE Main 2024

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. If 8 is replaced by 12, then the correct standard deviation is

(A) $\sqrt{3.86}$
(B) $1.8$
(C) $\sqrt{3.96}$
(D) $1.94$

Q30·MathematicsSingle correctJEE Main 2024

Let

a,b\in\mathbb{R}

. Let the mean and the variance of

6

observations

-3,4,7,-6,a,b

be

2

and

23

, respectively. The mean deviation about the mean of these

6

observations is:

(A) $\dfrac{13}{3}$
(B) $\dfrac{16}{3}$
(C) $\dfrac{11}{3}$
(D) $\dfrac{14}{3}$

Q31·MathematicsSingle correctJEE Main 2024

Consider 10 observations

x_1,x_2,\ldots,x_{10}

such that

\displaystyle\sum_{i=1}^{10}(x_i-\alpha)=2

and

\displaystyle\sum_{i=1}^{10}(x_i-\beta)^2=40

, where

\alpha,\beta

are positive integers. Let the mean and the variance of the observations be

\dfrac{6}{5}

and

\dfrac{84}{25}

respectively. The

\dfrac{\beta}{\alpha}

is equal to:

(A)2
(B) $\dfrac{3}{2}$
(C) $\dfrac{5}{2}$
(D)1

Q32·MathematicsSingle correctJEE Main 2024

If the median and mean deviation about the median of

170,125,230,190,210,a,b

be

170

and

\dfrac{205}{7}

respectively. Then the mean deviation about the mean of these

7

observations is:

(A) $31$
(B) $28$
(C) $30$
(D) $32$

Q33·MathematicsSingle correctJEE Main 2024

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+3b

is

(A)200
(B)190
(C)180
(D)210

Q34·MathematicsSingle correctJEE Main 2024

Let

M

denote the median of the following frequency distribution. Class:

0

-

4

,

4

-

8

,

8

-

12

,

12

-

16

,

16

-

20

; Frequency:

3

,

9

,

10

,

8

,

6

. Then

20M

is equal to:

(A)416
(B)104
(C)52
(D)208

Q35·MathematicsNumericalJEE Main 2024

The variance

\sigma^2

of the data |

x_i

| 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| |

f_i

| 3 | 2 | 3 | 2 | 6 | 3 | 3 | is ______.

Q36·MathematicsNumericalJEE Main 2024

If the mean and variance of the data

65,68,58,44,48,45,60,\alpha,\beta,60

where

\alpha>\beta

are 56 and 66.2 respectively, then

\alpha^2+\beta^2

is equal to ______.

Q37·MathematicsSingle correctJEE Main 2024

If the mean and variance of five observations are

\dfrac{24}{5}

and

\dfrac{194}{25}

respectively and the mean of first four observations is

\dfrac{7}{2}

, then the variance of the first four observations is equal to:

(A) $\dfrac{4}{5}$
(B) $\dfrac{77}{12}$
(C) $\dfrac{5}{4}$
(D) $\dfrac{105}{4}$

Q38·MathematicsNumericalJEE Main 2024

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12. If

\mu

and

\sigma^2

denote the mean and variance of the correct observations respectively, then

15(\mu+\mu^2+\sigma^2)

is equal to __________.

Q39·MathematicsSingle correctJEE Main 2024

Let

a_1,a_2,\ldots,a_{10}

be 10 observations such that

\displaystyle\sum_{k=1}^{10}a_k=50

and

\displaystyle\sum_{\forall k<j}a_k\,a_j=1100

. Then the standard deviation of

a_1,a_2,\ldots,a_{10}

is equal to:

(A)5
(B) $\sqrt5$
(C)10
(D) $\sqrt{115}$

Q40·MathematicsSingle correctJEE Advanced 2023

Consider the given data with frequency distribution

x_i

3 8 11 10 5 4

f_i

5 2 3 2 4 4 Match each entry in List-I to the correct entries in List-II. The correct option is:

List – I	List – II
P.The mean of the above data is	1.2.5
Q.The median of the above data is	2.5
R.The mean deviation about the mean of the above data is	3.6
S.The mean deviation about the median of the above data is	4.2.7
	5.2.4

(A)(P) → (3) (Q) → (2) (R) → (4) (S) → (5)
(B)(P) → (3) (Q) → (2) (R) → (1) (S) → (5)
(C)(P) → (2) (Q) → (3) (R) → (4) (S) → (1)
(D)(P) → (3) (Q) → (3) (R) → (5) (S) → (5)

Q41·MathematicsSingle correctJEE Main 2023

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:

(A)14
(B)13
(C)12
(D)11

Q42·MathematicsNumericalJEE Main 2023

Let the mean of the data:

\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 3 & 5 & 7 & 9 \\\hline \text{Frequency }(f) & 4 & 24 & 28 & \alpha & 8 \\\hline\end{array}

be

5

. If

m

and

\sigma^{2}

are respectively the mean deviation about the mean and the variance of the data, then

\dfrac{3\alpha}{m+\sigma^{2}}

is equal to _____.

Q43·MathematicsNumericalJEE Main 2023

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

Q44·MathematicsSingle correctJEE Main 2023

Two dice A and B are rolled. Let the numbers obtained on A and B be

\alpha

and

\beta

respectively. If the variance of

\alpha-\beta

is

\dfrac{p}{q}

, where p and q are co-prime, then the sum of the positive divisors of p is equal to

(A)36
(B)48
(C)31
(D)72

Q45·MathematicsSingle correctJEE Main 2023

If the mean of the observations

1,2,4,5,x

and

y

be

5

and their variance be

10

, then their mean deviation about the mean is equal to

(A) $\dfrac{10}{3}$
(B) $\dfrac{7}{3}$
(C) $3$
(D) $\dfrac{8}{3}$

Q46·MathematicsSingle correctJEE Main 2023

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 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is _______.

(A)32
(B)38
(C)40
(D)36

Q47·MathematicsSingle correctJEE Main 2023

Let

\mu

be the mean and

\sigma

be the standard deviation of the distribution with values

x_i=0,1,2,3,4,5

and frequencies

f_i=k+2,\,2k,\,k^2-1,\,k^2-1,\,k^2+1,\,k-3

respectively, where

\sum f_i=62

. If

[x]

denotes the greatest integer

\le x

, then

[\mu^2+\sigma^2]

is equal to:

(A) $8$
(B) $7$
(C) $6$
(D) $9$

Q48·MathematicsNumericalJEE Main 2023

If the mean of the frequency distribution — Class: 0-10, 10-20, 20-30, 30-40, 40-50; Frequency: 2, 3, x, 5, 4 — is 28, then its variance is _________.

Q49·MathematicsNumericalJEE Main 2023

Let the mean and variance of 8 numbers

x

,

y

, 10, 12, 6, 12, 4, 8, be 9 and 9.25 respectively. If

x>y

, then

3x-2y

is equal to

Q50·MathematicsSingle correctJEE Main 2023

Let the mean and variance of 12 observations be

\dfrac{9}{2}

and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is

\dfrac{m}{n}

, where m and n are co-prime, then m+n is equal to

(A)316
(B)314
(C)317
(D)315

Q51·MathematicsSingle correctJEE Main 2023

The mean and variance of a set of

15

numbers are

12

and

14

respectively. The mean and variance of another set of

15

numbers are

14

and

\sigma^2

respectively. If the variance of all the

30

numbers in the two sets is

13

, then

\sigma^2

is equal to:

(A) $9$
(B) $12$
(C) $11$
(D) $10$

Q52·MathematicsNumericalJEE Main 2023

If the mean and variance of the frequency distribution

x_i = 2,4,6,8,10,12,14,16

with frequencies

f_i = 4,4,\alpha,15,8,\beta,4,5

are 9 and 15.08 respectively, then the value of

\alpha^2+\beta^2-\alpha\beta

is

Q53·MathematicsSingle correctJEE Main 2023

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,\ldots,x_7

is 4 and mean is

\bar x

, then

\bar x+x_6

is equal to:

(A) $2\left(9+\dfrac{8}{\sqrt7}\right)$
(B) $18\left(1+\dfrac{1}{\sqrt3}\right)$
(C) $25$
(D) $34$

Q54·MathematicsSingle correctJEE Main 2023

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

(A) $1216$
(B) $1072$
(C) $1456$
(D) $1792$

Q55·MathematicsSingle correctJEE Main 2023

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and

\alpha\,(>0)

, and the mean and standard deviation of marks of class B of

n

students be respectively 55 and

30-\alpha

. If the mean and variance of the marks of the combined class of

100+n

students are respectively 50 and 350, then the sum of variances of classes

A

and

B

is:

(A) $650$
(B) $450$
(C) $900$
(D) $500$

Q56·MathematicsNumericalJEE Main 2023

If the variance of the frequency distribution with values

x_i = 2, 3, 4, 5, 6, 7, 8

and corresponding frequencies

f_i = 3, 6, 16, \alpha, 9, 5, 6

is 3, then

\alpha

is equal to

Q57·MathematicsSingle correctJEE Main 2023

Let

S

be the set of all values of

a_1

for which the mean deviation about the mean of 100 consecutive positive integers

a_1, a_2, a_3, \ldots, a_{100}

is

25

. Then

S

is:

(A) $\mathbb{N}$
(B) $\phi$
(C) $\{99\}$
(D) $\{9\}$

Q58·MathematicsNumericalJEE Main 2023

The mean and variance of

7

observations are

8

and

16

respectively. If one observation

14

is omitted and

a

and

b

are respectively mean and variance of remaining

6

observation, then

a+3b-5

is equal to

Q59·MathematicsNumericalJEE Main 2023

Let

X=\{11,12,13,\dots,40,41\}

and

Y=\{61,62,63,\dots,90,91\}

be the two sets of observations. If

\bar x

and

\bar y

are their respective means and

\sigma^2

is the variance of all the observations in

X\cup Y

, then

|\bar x+\bar y-\sigma^2|

is equal to _____.

Q60·MathematicsSingle correctJEE Main 2023

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:

(A) $3.96$
(B) $4.08$
(C) $4.04$
(D) $3.92$

Q61·MathematicsSingle correctJEE Main 2023

Let the six numbers

a_1,a_2,a_3,a_4,a_5,a_6

be in A.P. and

a_1+a_3=10

. If the mean of these six numbers is

\dfrac{19}{2}

and their variance is

\sigma^2

, then

8\sigma^2

is equal to:

(A) $210$
(B) $220$
(C) $200$
(D) $105$

Q62·MathematicsNumericalJEE Main 2022

Let the mean and the variance of 20 observations

x_{1},\,x_{2},\ldots x_{20}

be 15 and 9, respectively. For

\alpha \in R

, if the mean of

\left(x_{1}+\alpha\right)^{2},\,\left(x_{2}+\alpha\right)^{2},\ldots,\,\left(x_{20}+\alpha\right)^{2}

is 178, then the square of the maximum value of

\alpha

is equal to __________.

Q63·MathematicsNumericalJEE Main 2022

Let

x_{1}

,

x_{2}

,

x_{3}

, …..,

x_{20}

be in geometric progression with

x_{1} = 3

and the common ration

\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 new data, then the greatest integer less than or equal to

\bar{x}

is __________.

Q64·MathematicsNumericalJEE Main 2022

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 __________.

Q65·MathematicsNumericalJEE Main 2022

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____________.

Q66·MathematicsSingle correctJEE Main 2022

Let the mean and the variance of 5 observations

x_1, x_2, x_3, x_4, x_5

be

\frac{24}{5}

and

\frac{194}{25}

respectively. If the mean and variance of the first 4 observation are

\frac{7}{2}

and

a

respectively, then

(4a + x_5)

is equal to:

(A)13
(B)15
(C)17
(D)18

Q67·MathematicsSingle correctJEE Main 2022

The number of values of

a \in \mathbb{N}

such that the variance of 3, 7, 12

a

,

43 - a

is a natural number is:

(A)0
(B)2
(C)5
(D)infinite

Q68·MathematicsNumericalJEE Main 2022

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

Q69·MathematicsNumericalJEE Main 2022

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 ______.

Q70·MathematicsSingle correctJEE Main 2022

The mean and variance of the data4, 5, 6, 6, 7, 8, x, y where

x<y

are 6, and

\dfrac{9}{4}

respectively. Then

x^{4}+y^{2}

is equal to

(A)162
(B)320
(C)674
(D)420

Q71·MathematicsSingle correctJEE Main 2022

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:

(A) $60$
(B) $55$
(C) $50$
(D) $45$

Q72·MathematicsSingle correctJEE Main 2022

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 variance is equal to :

(A)10
(B)36
(C)43
(D)60

Q73·MathematicsNumericalJEE Main 2022

If the mean deviation about the mean of the numbers 1, 2, 3, ....., n, where n is odd, is

\frac{5(n + 1)}{n}

, then n is equal to ______

Q74·MathematicsSingle correctJEE Main 2021

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 :

(A) $\frac{92}{5}$
(B) $\frac{134}{5}$
(C) $\frac{536}{25}$
(D) $\frac{112}{5}$

Q75·MathematicsNumericalJEE Main 2021

The mean of 10 numbers

7 \times 8,\ 10 \times 10,\ 13 \times 12,\ 16 \times 14,\ \ldots.

is ______.

Q76·MathematicsNumericalJEE Main 2021

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 μ is the average marks of girls and

\sigma^{2}

is the variance of marks of 50 candidates, then

\mu + \sigma^{2}

is equal to _________ .

Q77·MathematicsNumericalJEE Main 2021

Let

n

be an odd natural number such that the variance of

1, 2, 3, 4, ..., n

is 14. Then

n

is equal to ________.

Q78·MathematicsSingle correctJEE Main 2021

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 deviation respectively for correct data, then

(\alpha, \beta)

is :

(A) $(11, 26)$
(B) $(10.5, 25)$
(C) $(11, 25)$
(D) $(10.5, 26)$

Q79·MathematicsNumericalJEE Main 2021

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 ________.

Q80·MathematicsSingle correctJEE Main 2021

Let the mean and variance of the frequency distribution x: x

_1

= 2, x

_2

= 6, x

_3

= 8, x

_4

= 9 f: 4, 4, α, β be 6 and 6.8 respectively. If x

_3

is changed from 8 to 7, then the mean for the new data will be :

(A)4
(B)5
(C) $\frac{17}{3}$
(D) $\frac{16}{3}$

Q81·MathematicsSingle correctJEE Main 2021

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

\left(a-b\right)^2

is equal to :

(A)32
(B)24
(C)12
(D)16

Q82·MathematicsNumericalJEE Main 2021

Consider the following frequency distribution : Class : 10-20, 20-30, 30-40, 40-50, 50-60; Frequency :

\alpha

, 110, 54, 30,

\beta

. If the sum of all frequencies is 584 and median is 45, then

\left| \alpha - \beta \right|

is equal to.......

Q83·MathematicsSingle correctJEE Main 2021

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 :

(A)4
(B)6
(C)5
(D)8

Q84·MathematicsNumericalJEE Main 2021

Consider the following frequency distribution : Class : 0 – 6 6 – 12 12 – 18 18 – 24 24 – 30 Frequency : a b 12 9 5 If mean =

\frac{309}{22}

and median = 14, then the value

(a - b)^2

is equal to..................

Q85·MathematicsSingle correctJEE Main 2021

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 :

(A)10, 11
(B)3, 18
(C)1, 20
(D)8, 13

Q86·MathematicsSingle correctJEE Main 2021

If the mean and variance of six observations

7,\ 10,\ 11,\ 15,\ a,\ b

are

10

and

\frac{20}{3}

, respectively, then the value of

|a-b|

is equal to

(A) $9$
(B) $7$
(C) $11$
(D) $1$

Q87·MathematicsSingle correctJEE Main 2021

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 :

(A)425
(B)650
(C)250
(D)925

Q88·MathematicsNumericalJEE Main 2021

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 appointed teacher is_.

Q89·MathematicsNumericalJEE Main 2021

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 the remaining

n

numbers. If the variance of the new set is

k

, then

9k

is equal to ______.

Q90·MathematicsNumericalJEE Main 2021

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 these two observations is

\frac{17}{9}

, then the value of n is equal to _________.

Q91·MathematicsSingle correctJEE Main 2021

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 ?

(A) $b^{2} = 3(a^{2} + c^{2}) + 9d^{2}$
(B) $b^{2} = a^{2} + c^{2} + 3d^{2}$
(C) $b^{2} = 3(a^{2} + c^{2} + d^{2})$
(D) $b^{2} = 3(a^{2} + c^{2}) - 9d^{2}$

Q92·MathematicsNumericalJEE Main 2021

Let

X_{1}

,

X_{2}

,………..

X_{18}

be eighteen observation such that

\sum_{i=1}^{18}\left(X_{i}-\alpha\right) = 36

and

\sum_{i=1}^{18}\left(X_{i}-\beta\right)^{2} = 90

, where

\alpha

and

\beta

are distinct real numbers. If the standard deviation of these observations is 1, then the value of

|\alpha - \beta|

is ________________.

Q93·MathematicsNumericalJEE Main 2021

If the variance of 10 natural numbers

1,1,1,\ldots,1,k

is less than 10, then the maximum possible value of

k

is__________.

Q94·MathematicsSingle correctJEE Main 2020

If

\displaystyle\sum_{i=1}^{n}(x_i-a) = n

and

\displaystyle\sum_{i=1}^{n}(x_i-a)^2 = na,\ (n,a>1)

then the standard deviation of n observations

x_1, x_2, \ldots, x_n

is:

(A) $a-1$
(B) $n\sqrt{a-1}$
(C) $\sqrt{n(a-1)}$
(D) $\sqrt{a-1}$

Q95·MathematicsNumericalJEE Main 2020

Consider the data on x taking the values

0, 2, 4, 8, \ldots, 2^n

with frequencies

^{n}C_0

,

^{n}C_1

,

^{n}C_2

,

\ldots

,

^{n}C_n

respectively. If the mean of this data is

\frac{728}{2^n}

, then n is equal to __________.

Q96·MathematicsSingle correctJEE Main 2020

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is:

(A)2
(B)4
(C)1
(D)3

Q97·MathematicsSingle correctJEE Main 2020

If the mean and standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation:

(A) $x^2 - 10x + 19 = 0$
(B) $x^2 - 20x + 18 = 0$
(C) $x^2 - 10x + 18 = 0$
(D) $2x^2 - 20x + 19 = 0$

Q98·MathematicsNumericalJEE Main 2020

If the variance of the following frequency distribution : is 50, then x is equal to:

Class	10 – 20	20 – 30	30 – 40
Frequency	2	x	2

Q99·MathematicsSingle correctJEE Main 2020

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is:

(A) $3$
(B) $5$
(C) $7$
(D) $9$

Q100·MathematicsSingle correctJEE Main 2020

Let

x_i \left( 1 \le i \le 10 \right)

be ten observations of a random variable X. If

\sum_{i=1}^{10} \left( x_i - p \right) = 3

and

\sum_{i=1}^{10} \left( x_i - p \right)^2 = 9

where

0 \ne p \in R

, then the standard deviation of these observations is:

(A) $\sqrt{\frac{3}{5}}$
(B) $\frac{4}{5}$
(C) $\frac{7}{10}$
(D) $\frac{9}{10}$

Q101·MathematicsSingle correctJEE Main 2020

For the frequency distribution: Variate (x):

x_{1}

x_{2}

x_{3}

....

x_{15}

Frequency (f):

f_{1}

f_{2}

f_{3}

....

f_{15}

Where

0<x_{1}<x_{2}<x_{3}<\ldots<x_{15}=10

and

\sum\limits_{i=1}^{15}f_{i}>0

, the standard deviation cannot be:

(A)4
(B)2
(C)6
(D)1

Q102·MathematicsSingle correctJEE Main 2020

Let the observations

x_i

(1\le i\le10)

satisfy the equation

\displaystyle\sum_{i=1}^{10}(x_i-5)=10

and

\displaystyle\sum_{i=1}^{10}(x_i-5)^2=40

. If

\mu

and

\lambda

are the mean and the variance of the observations,

x_1-3,x_2-3,……………,x_{10}-3

, then the ordered pair

(\mu,\lambda)

is equal to:

(A)(6, 6)
(B)(3, 3)
(C)(3, 6)
(D)(6, 3)

Q103·MathematicsSingle correctJEE Main 2020

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:

(A)4.02
(B)3.98
(C)4.01
(D)3.99

Q104·MathematicsNumericalJEE Main 2020

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

Q105·MathematicsNumericalJEE Main 2020

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 _________

Q106·MathematicsSingle correctJEE Main 2019

If the data

x_{1}, x_{2}, ...., x_{10}

is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000; then the standard deviation of this data is :

(A) $2\sqrt{2}$
(B)2
(C)4
(D) $\sqrt{2}$

Q107·MathematicsSingle correctJEE Main 2019

If for some x

\in

R, the frequency distribution of the marks obtained by 20 students in a test is Then the mean of the marks is:

Marks	2	3	5	7
Frequency	$(x+1)^{2}$	2x − 5	$x^{2}-3x$	x

(A)2.8
(B)3.2
(C)2.5
(D)3.0

Q108·MathematicsSingle correctJEE Main 2019

If both the means and the standard deviation of 50 observations

x_1

,

x_2

, ………,

x_{50}

are equal to 16, then the mean of

(x_1 - 4)^{2}

,

(x_2 - 4)^{2}

, ….,

(x_{50} - 4)^{2}

is

(A)400
(B)380
(C)525
(D)480

Q109·MathematicsSingle correctJEE Main 2019

If the standard deviation of the numbers

-1,0,1,k

is

\sqrt{5}

where

k>0

, then k is equal to:

(A) $4\sqrt{\dfrac{5}{3}}$
(B) $\sqrt{6}$
(C) $2\sqrt{6}$
(D) $2\sqrt{\dfrac{10}{3}}$

Q110·MathematicsSingle correctJEE Main 2019

The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then

\dfrac{y}{x}

is equal to

(A) $\dfrac{7}{3}$
(B) $\dfrac{9}{4}$
(C) $\dfrac{7}{2}$
(D) $\dfrac{8}{3}$

Q111·MathematicsSingle correctJEE Main 2019

A student score 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:

(A) $\frac{10}{3}$
(B) $\frac{100}{3}$
(C) $\frac{100}{\sqrt{3}}$
(D) $\frac{10}{\sqrt{3}}$

Q112·MathematicsSingle correctJEE Main 2019

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the product of the remaining two observations is:

(A)40
(B)45
(C)49
(D)48

Q113·MathematicsSingle correctJEE Main 2019

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is:

(A)30
(B)51
(C)50
(D)31

Q114·MathematicsSingle correctJEE Main 2019

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is :

(A)7
(B)5
(C)1
(D)3

Q115·MathematicsSingle correctJEE Main 2019

The outcome of each of 30 items was observed; 10 items gave an outcome

\dfrac{1}{2}-d

each, 10 items gave outcome

\dfrac{1}{2}

each and the remaining 10 items gave outcome

\dfrac{1}{2}+d

each. If the variance of this outcome data is

\dfrac{4}{3}

then

|d|

equals:

(A) $\dfrac{2}{3}$
(B)2
(C) $\dfrac{\sqrt{5}}{2}$
(D) $\sqrt{2}$

Q116·MathematicsSingle correctJEE Main 2019

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is:

(A)10 : 3
(B)4 : 9
(C)5 : 8
(D)6 : 7

Q117·MathematicsSingle correctJEE Main 2019

A data consists of n observations:

x_{1},x_{2},......,x_{n}

. If

\displaystyle\sum_{i=1}^{n}(x_{i}+1)^{2}=9n

and

\displaystyle\sum_{i=1}^{n}(x_{i}-1)^{2}=5n

, then the standard deviation of this data is:

(A)5
(B) $\sqrt{5}$
(C) $\sqrt{7}$
(D)2

Q118·MathematicsSingle correctJEE Main 2019

5 students of a class have an average height 150 cm and variance 18

cm^{2}

. A new student, whose height is 156 cm, joined them. The variance (in

cm^{2}

) of the height of these six students is:

(A)16
(B)22
(C)20
(D)18

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