Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · Mathematics · Statistics

JEE Statistics PYQs with Solutions

323 previous year questions from Statistics (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

323 questionsMathematics2002–2026Answers + solutions

About Statistics PYQs

Statistics has 323 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (164), NTA Abhyas JEE Main (52) and JEE Advanced (4), spanning 2002 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 17
  • 2025: 9
  • 2024: 18
  • 2023: 22
  • 2022: 12
  • 2021: 20
  • 2020: 67
  • 2019: 14
  • 2018: 5
  • 2017: 3
  • 2016: 3
  • 2015: 2

Statistics questions with solutions

1

Consider a data consisting of 10 observations x_1, x_2, …, 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, …, x_8

JEE Advanced 2026 Solution View → 2

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:

JEE Main 2026 Solution View → 3

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 :

JEE Main 2026 Solution View → 4

A data consists of 20 observations x_1, x_2, …, x_ 20 . If ∑_ i=1 ^ 20 (x_i + 5)^2 = 2500 and ∑_ i=1 ^ 20 (x_i - 5)^2 = 100 , then the ratio of mean to standard deviation of this

JEE Main 2026 Solution View → 5

A variable X takes values 0, 0, 2, 6, 12, 20, …, n(n-1) with frequencies ^nC_0, ^nC_1, ^nC_2, ^nC_3, ^nC_4, ^nC_5, …, ^nC_n , respectively. If the mean of this data is 60 , then

JEE Main 2026 Solution View → 6

The mean deviation about the mean for the data x_i 5 7 9 10 12 15 f_i 8 6 2 2 2 6 is equal to:

JEE Main 2026 Solution View → 7

For 10 observations x_1, x_2, …, x_ 10 , if ∑_ i=1 ^ 10 (x_i+2)^2=180 and ∑_ i=1 ^ 10 (x_i-1)^2=90 , then their standard deviation is:

JEE Main 2026 Solution View → 8

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

JEE Main 2026 Solution View → 9

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

JEE Main 2026 Solution View → 10

If the mean of the data Class 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 2 k 28 54 k+1 5 is 21 , then k is one of the roots of the equation :

JEE Main 2026 Solution View → 11

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

JEE Main 2026 Solution View → 12

Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈ X\ . If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible

JEE Main 2026 Solution View → 13

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

JEE Main 2026 Solution View → 14

If the mean and the variance of the data \( Class 4-8 8-12 12-16 16-20 Frequency 3 λ 4 7 \) are μ and 19 respectively, then the value of λ+μ is

JEE Main 2026 Solution View → 15

Let the mean and variance of 8 numbers -10,-7,-1, x, y, 9,2,16 be (7)/(2) and (293)/(4) , respectively. Then the mean of 4 numbers x, y, x+y+1,|x-y| is :

JEE Main 2026 Solution View → 16

If the mean deviation about the median of the numbers k, 2 k, 3 k, …. ., 1000 k is 500, then k^ 2 is equal to :

JEE Main 2026 Solution View → 17

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 another without

JEE Main 2026 Solution View → 18

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

JEE Advanced 2025 Solution View → 19

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

JEE Main 2025 Solution View → 20

Let the mean and the standard deviation of the observation 2,3,3,4,5,7 , a, b be 4 and 2 respectively. Then the mean deviation about the mode of these observations is :

JEE Main 2025 Solution View → 21

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, … … . .5 is

JEE Main 2025 Solution View → 22

If the mean and the variance of 6,4, a, 8, b, 12,10 , 13 are 9 and 9.25 respectively, then a+b+a b is equal to :

JEE Main 2025 Solution View → 23

Let \(x_1, x_2, …, x_ 10 \) be ten observations such that \(∑_ i=1 ^ 10 (x_i-2)=30, ∑_ i=1 ^ 10 (x_i- β)^ 2=98, β 2\), and their variance is \( (4)/(5) . If \(μ\) and \(σ^ 2\) are

JEE Main 2025 Solution View → 24

For a statistical data x_1, x_2, …, x_ 10 of 10 values, a student obtained the mean as 5.5 and ∑_ i=1 ^ 10 x_i^2=371 . He later found that he had noted two values in the data

JEE Main 2025 Solution View → 25

The variance of the numbers 8,21,34,47, …, 320 is

JEE Main 2025 Solution View → 26

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class

JEE Main 2025 Solution View → 27

Let X be a random variable, and let P(X=x) denote the probability that X takes the value x . Suppose that the points (x, P(X=x)), x=0,1,2,3,4 , lie on a fixed straight line in the

JEE Advanced 2024 Solution View → 28

If the variance of the frequency distribution array |c|c|c|c|c|c|c| x & c & 2 c & 3 c & 4 c & 5 c & 6 c f & 2 & 1 & 1 & 1 & 1 & 1 array is 160, then the value ofc ∈ N is

JEE Main 2024 Solution View → 29

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

JEE Main 2024 Solution View → 30

Let a, b, c ∈ 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 (136)/(5) , respectively. Then 2

JEE Main 2024 Solution View → 31

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.

JEE Main 2024 Solution View → 32

Let the mean and the standard deviation of the probability distribution array |c|c|c|c|c| X & α & 1 & 0 & -3 P ( X) & (1)/(3) & ~K & (1)/(6) & (1)/(4) array be μ and σ

JEE Main 2024 Solution View → 33

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If

JEE Main 2024 Solution View → 34

If the mean of the following probability distribution of a random variable X : array |c|c|c|c|c|c| X & 0 & 2 & 4 & 6 & 8 P ( X) & a & 2 a & a+b & 2 b & 3 b array is (46)/(9)

JEE Main 2024 Solution View → 35

Let α, β ∈ R . Let the mean and the variance of 6 observations -3,4,7,-6, α, β be 2 and 23 , respectively. The mean deviation about the mean of these 6 observations is :

JEE Main 2024 Solution View → 36

Consider 10 observation x _ 1 , x _ 2 , . .. x _ 10 , such that ∑ _ i = 1 ^ 10 ( x _ i - α) = 2 and ∑ _ i = 1 ^ 10 ( x _ i - β) ^ 2 = 40 , where α, β are positive integers. Let

JEE Main 2024 Solution View → 37

Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and (205)/(7) respectively. Then the mean deviation about the mean of

JEE Main 2024 Solution View → 38

Let the mean and the variance of 6 observation a, b, 68, 44, 48, 60 be 55 and 194 , respectively if a > b , then a + 3b is

JEE Main 2024 Solution View → 39

If the variance σ ^ 2 of the data cases x _ i & 0 & 1 & 5 & 6 & 10 & 12 & 17 f _ i & 3 & 2 & 3 & 2 & 6 & 3 & 3 cases is k then the value of [k] is ______ where [.] denotes the

JEE Main 2024 Solution View → 40

Let M denote the median of the following frequency distribution. cases Class & 0 - 4 & 4 - 8 & 8 - 12 & 12 - 16 & 16 - 20 Frequency & 3 & 9 & 10 & 8 & 6 cases Then 20M is equal to

JEE Main 2024 Solution View → 41

If the mean and variance of five observations are (24)/(5) and (194)/(25) respectively and the mean of first four observations is (7)/(2) , then the variance of the first four

JEE Main 2024 Solution View → 42

If the mean and variance of the data 65, 68, 58, 44 , 48, 45, 60, α, β, 60 where α > β are 56 and 66 . 2 respectively, then α ^ 2 + β ^ 2 is equal to

JEE Main 2024 Solution View → 43

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 μ and

JEE Main 2024 Solution View → 44

Let a _ 1 , a _ 2 , . . . , a _ 10 be 10 observations such that ∑ _ k = 1 ^ 10 a _ k = 50 and ∑ _ ∀ k < j a _ k · a _ j = 1100 . Then the standard deviation of a _ 1 , a _ 2 , …

JEE Main 2024 Solution View → 45

Consider the given data with frequency distribution cases x _ i & 3 & 8 & 11 & 10 & 5 & 4 f _ i & 5 & 2 & 3 & 2 & 4 & 4 cases Match each entry in List-I to the correct entries in

JEE Advanced 2023 Solution View → 46

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

JEE Main 2023 Solution View → 47

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

JEE Main 2023 Solution View → 48

Let the mean of the data x 1 3 5 7 9 Frequency (f) 4 24 28 α 8 be 5 . If m and σ ^ 2 are respectively the mean deviation about the mean and the variance of the data, then 3α m + σ

JEE Main 2023 Solution View → 49

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 (31)/(10) and (m)/(n) respectively, where m and n are co-prime. If the

JEE Main 2023 Solution View → 50

Let the mean of 6 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

JEE Main 2023 Solution View → 51

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

JEE Main 2023 Solution View → 52

Let μ be the mean and σ be the standard deviation of the distribution X _ i 0 1 2 3 4 5 f _ i k + 2 2k k ^ 2 - 1 k ^ 2 - 1 k ^ 2 + 1 k - 3 where Σ f _ i = 62 . If [x] denotes the

JEE Main 2023 Solution View → 53

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 ________ .

JEE Main 2023 Solution View → 54

Let the mean and variance of 12 observations be (9)/(2) and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14

JEE Main 2023 Solution View → 55

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 _______

JEE Main 2023 Solution View → 56

If the mean and variance of the frequency distribution x _ i 2 4 6 8 10 12 14 16 f _ i 4 4 α 15 8 β 4 5 are 9 and 15 . 08 respectively, then the value of α ^ 2 + β ^ 2 - αβ is

JEE Main 2023 Solution View → 57

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 σ ^ 2 respectively. If the variance of all

JEE Main 2023 Solution View → 58

Let 9 = x _ 1 < x _ 2 < … < 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 ¯ x , then ¯ x + x _ 6 is

JEE Main 2023 Solution View → 59

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

JEE Main 2023 Solution View → 60

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and α(> 0) , and the mean and standard deviation of marks of class B of n students be

JEE Main 2023 Solution View → 61

If the variance of the frequency distribution x _ i 2 3 4 5 6 7 8 Frequency f _ i 3 6 16 α 9 5 6 is 3 , then α is equal to

JEE Main 2023 Solution View → 62

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 , … . , a _ 100 is 25 . Then S is

JEE Main 2023 Solution View → 63

The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted, a and b are respectively mean and variance of remaining 6 observation, then a

JEE Main 2023 Solution View → 64

Let X = \ 11, 12, 13, … . , 40, 41\ and Y =\ 61, 62, 63, . . . , 90, 91\ be the two sets of observations. If ¯ x and ¯ y are their respective means and σ ^ 2 is the variance of

JEE Main 2023 Solution View → 65

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

JEE Main 2023 Solution View → 66

Let the six numbers a _ 1 , a _ 2 , . . . , a _ 6 be in A . P . and a _ 1 + a _ 3 = 10 .If the mean of these six numbers is (19)/(2) and their variance is σ ^ 2 , then 8 σ ^ 2 is

JEE Main 2023 Solution View → 67

Let the mean and the variance of 20 observations x _ 1 , x _ 2 , … x _ 20 be 15 and 9 , respectively. For α ∈ R , if the mean of ( x _ 1 + α) ^ 2 , ( x _ 2 + α) ^ 2 , … , ( x _ 20

JEE Main 2022 Solution View → 68

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

JEE Main 2022 Solution View → 69

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 σ is the standard

JEE Main 2022 Solution View → 70

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

JEE Main 2022 Solution View → 71

The number of values of a ∈ N such that the variance of 3, 7, 12, a, 43 - a is a natural number is:

JEE Main 2022 Solution View → 72

Let the mean and the variance of 5 observations x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ 5 be (24)/(5) and (194)/(25) respectively. If the mean and variance of the first 4 observation

JEE Main 2022 Solution View → 73

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

JEE Main 2022 Solution View → 74

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

JEE Main 2022 Solution View → 75

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

JEE Main 2022 Solution View → 76

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

JEE Main 2022 Solution View → 77

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 25M is equal to

JEE Main 2022 Solution View → 78

If the mean deviation about the mean of the numbers 1, 2, 3, … … , n , where n is odd, is (5(n + 1))/(n) , then n is equal to ______.

JEE Main 2022 Solution View → 79

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

JEE Main 2021 Solution View → 80

The mean of 10 numbers 7 × 8, 10 × 10, 13 × 12, 16 × 14, … is

JEE Main 2021 Solution View → 81

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

JEE Main 2021 Solution View → 82

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

JEE Main 2021 Solution View → 83

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 ______.

JEE Main 2021 Solution View → 84

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 α

JEE Main 2021 Solution View → 85

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

JEE Main 2021 Solution View → 86

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

JEE Main 2021 Solution View → 87

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 13 . 44

JEE Main 2021 Solution View → 88

Consider the following frequency distribution : class 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency α 110 54 30 β If the sum of all frequencies is 584 and median is 45 , then

JEE Main 2021 Solution View → 89

Consider the following frequency distribution: Class: 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30 Frequency: a b 12 9 5 If mean = (309)/(22) and median = 14, then the value ( a - b ) ^ 2

JEE Main 2021 Solution View → 90

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

JEE Main 2021 Solution View → 91

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:

JEE Main 2021 Solution View → 92

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

JEE Main 2021 Solution View → 93

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

JEE Main 2021 Solution View → 94

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

JEE Main 2021 Solution View → 95

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

JEE Main 2021 Solution View → 96

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

JEE Main 2021 Solution View → 97

Let X _ 1 , X _ 2 , … , X _ 18 be eighteen observations such that ∑ _ i = 1 ^ 18 ( X _ i - α) = 36 and ∑ _ i = 1 ^ 18 ( X _ i - β) ^ 2 = 90 , where α and β are distinct real

JEE Main 2021 Solution View → 98

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

JEE Main 2021 Solution View → 99

Consider the data on x taking the values 0, 2, 4, 8, . . . . . , 2 ^ n with frequencies C0 n , C1 n , C2 n , . . . . , Cn n respectively. If the mean of this data is 728 2 ^ n

JEE Main 2020 Solution View → 100

If Σ _ i = 1 ^ n ( x _ i - a) = n and Σ _ i = 1 ^ n ( x _ i - a) ^ 2 = na, (n, a > 1) , then the standard deviation of n observations x _ 1 , x _ 2 , … , x _ n is

JEE Main 2020 Solution View → 101

If the mean and the 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:

JEE Main 2020 Solution View → 102

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 :

JEE Main 2020 Solution View → 103

If the variance of the following frequency distribution: Class: 10 - 2020 - 3030 - 40 Frequency: 2x2 is 50, then x is equal to _______

JEE Main 2020 Solution View → 104

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

JEE Main 2020 Solution View → 105

Let x _ i (1 ≤ i ≤ 10) be ten observation of a random variable X . If ∑ _ i = 1 ^ 10 ( x _ i - p) = 3 and ∑ _ i = 1 ^ 10 ( x _ i - p) ^ 2 = 9 where 0 ≠ p ∈ R , then the standard

JEE Main 2020 Solution View → 106

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 0, the standard deviation cannot be

JEE Main 2020 Solution View → 107

If the variance of the terms in an increasing A . P . b _ 1 b _ 2 , b _ 3 , … … . . , b _ 11 is 90 then the common difference of this A . P . is

JEE Main 2020 Solution View → 108

Let X = \ x ∈ N: 1 ≤ x ≤ 17\ and Y = \ ax + b: x ∈ Xanda, b ∈ R, a > 0\ . If mean and variance of elements of Y are 17 and 216 respectively then a + b is equal to

JEE Main 2020 Solution View → 109

Let the observation x _ i (1 ≤ i ≤ 10) satisfy the equations ∑ _ i = 1 ^ 10 ( x _ i - 5) = 10 , ∑ _ i = 1 ^ 10 ( x _ i - 5) ^ 2 = 40 . If μ and λ are the mean and the variance of

JEE Main 2020 Solution View → 110

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

JEE Main 2020 Solution View → 111

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q

JEE Main 2020 Solution View → 112

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

JEE Main 2020 Solution View → 113

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

JEE Main 2020 Solution View → 114

The mean of a data set comprising of 16 observations is 16 . If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data

NTA Abhyas JEE Main 2020 Solution View → 115

The average of five consecutive odd numbers is 61. Then the difference between the highest and lowest numbers is

NTA Abhyas JEE Main 2020 Solution View → 116

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

NTA Abhyas JEE Main 2020 Solution View → 117

The variance of the numbers& 2, 3, 11 and x is (49)/(4) , then the values of x & are

NTA Abhyas JEE Main 2020 Solution View → 118

If the variance of the following data : 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 is K , then the value of (K)/(11) is

NTA Abhyas JEE Main 2020 Solution View → 119

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

NTA Abhyas JEE Main 2020 Solution View → 120

The mean and standard deviation of 100 observations were calculated as 40 and 5.1, respectively by a student who took by mistake 50 instead of 40 for one observation, then& the

NTA Abhyas JEE Main 2020 Solution View → 121

For a group of 50 male workers, the mean and the standard deviation of their daily wages are Rs. 630 and Rs. 90 respectively and for a group of 40 female workers these are Rs. 540

NTA Abhyas JEE Main 2020 Solution View → 122

The mean of five numbers is 0 and their variance is 2 . If three of those numbers are - 1, 1 and 2, then the other two numbers are

NTA Abhyas JEE Main 2020 Solution View → 123

If both the mean 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

NTA Abhyas JEE Main 2020 Solution View → 124

If the mean of 10 observations is 50 and the sum of the squares of the deviations of observations from the mean is 250 , then the coefficient of variation of those observations is

NTA Abhyas JEE Main 2020 Solution View → 125

Let one observation equal to the mean is added to n observations. If the variance changes from 78 to 72 , then n is equal to

NTA Abhyas JEE Main 2020 Solution View → 126

The mean and variance of a data set comprising 15 observations are 15 and 5 respectively. If one of the observation 15 is deleted and two new observations 6 and 8 are added to the

NTA Abhyas JEE Main 2020 Solution View → 127

In an experiment with 9 observations on x , the following results are available ∑ x^ 2 = 360 and ∑ x = 34 . One observation that was 8, was found to be wrong and was replaced by

NTA Abhyas JEE Main 2020 Solution View → 128

If ∑ _ i = 1 ^ 5 ( x _ i - 6) = 5 and ∑ _ i = 1 ^ 5 ( x _ i - 6) ^ 2 = 25 , then the standard deviation of observations 3 x _ 1 + 2,3 x _ 2 + 2,3 x _ 3 + 2, 3 x _ 4 + 2 and 3 x _

NTA Abhyas JEE Main 2020 Solution View → 129

The mean and variance of seven& observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12 and 14 , then the remaining two& observations are

NTA Abhyas JEE Main 2020 Solution View → 130

If x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ 5 ....... x _ n are n observations such that ∑ _ i = 1 ^ n x _i^ 2 = 400 and ∑ _ i = 1 ^ n x _ i = 100, then the possible value of n among

NTA Abhyas JEE Main 2020 Solution View → 131

The mean and variance of 20 observations are found to be 10 and 4 respectively. On rechecking, it was found that an observation 8 is incorrect. If the wrong observation is

NTA Abhyas JEE Main 2020 Solution View → 132

The mean and variance of 10 observations are found to be 10 and 4 respectively. On rechecking it was found that an observation 8 was incorrect. If it is replaced by 18, then the

NTA Abhyas JEE Main 2020 Solution View → 133

If for a sample size of 10, &#8721; _ i = 1 ^ 10 ( x _ i - 5)^ 2 = 350 and &#8721; _ i = 1 ^ 10 ( x _ i - 6) =20 , then the variance is

NTA Abhyas JEE Main 2020 Solution View → 134

If the standard deviation of 0, 1, 2,... , 9 is k , then the standard deviation of 10, 11, 12,... , 19 is

NTA Abhyas JEE Main 2020 Solution View → 135

Let x _ 1 , x _ 2 , x _ 3 .... x _ k be k observations and w _ i = a x _ i + b for i = 1,2, 3..... k , where a and b are constants. If mean of x _ i is 52 and their standard

NTA Abhyas JEE Main 2020 Solution View → 136

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

NTA Abhyas JEE Main 2020 Solution View → 137

A number equal to 2 times the mean and with a frequency equal to k is inserted in a data having n observations. If the new mean is (4)/(3) times the old mean, then the value of

NTA Abhyas JEE Main 2020 Solution View → 138

The means of two samples of size 40 and 50 were found to be 54 and 63 respectively. Their standard deviations were 6 and 9 respectively. The variance of the combined sample of

NTA Abhyas JEE Main 2020 Solution View → 139

The mean and standard deviation of 10 observations x _ 1 , x _ 2 , x _ 3 ..... x _ 10 are ¯ x and σ respectively. Let 10 is added to x _ 1 , x _ 2 ..... x _ 9 and 90 is subtracted

NTA Abhyas JEE Main 2020 Solution View → 140

If the mean of 10 observations is 50 and the sum of the squares of the deviations of observations from the mean is 250 , then the coefficient of variation of these observations is

NTA Abhyas JEE Main 2020 Solution View → 141

If x _ 1 , x _ 2 , x _ 3 ... x _ 34 are numbers such that x _ i = x _ i + 1 = 150, ∀ i ∈ \ 1,2, 3,4,.... 9\ and x _ i + 1 - x _ i = - 2, ∀ i ∈ \ 10,11,.... 33\ , then median of x

NTA Abhyas JEE Main 2020 Solution View → 142

The variance of the first 20 positive integral multiples of 4 is equal to

NTA Abhyas JEE Main 2020 Solution View → 143

The ratio of the variance of first n positive integral multiples of 4 to the variance of first n positive odd numbers is

NTA Abhyas JEE Main 2020 Solution View → 144

Let V _ 1 = variance of \ 13,16,19 . . . . . . . . . . 103\ ~and V _ 2 = variance of \ 20,26,32 . . . . . . . . . . 200\ . Then V _ 1 : V _ 2 is

NTA Abhyas JEE Main 2020 Solution View → 145

The mean square deviation of a set of observations& x _ 1 , x _ 2 . . . . . . x _ n about a point m is defined as (1)/(n) ∑ _ i = 1 ^ n ( x _ i - m)2 . If the mean square

NTA Abhyas JEE Main 2020 Solution View → 146

If 2 data sets having 10 and 20 observations have coefficients of variation 50 and 60 respectively and arithmetic means 30 and 25 respectively, then the combined variance of those

NTA Abhyas JEE Main 2020 Solution View → 147

If the mean and the variance of the numbers a, b, 8,5 and 10 are 6 and 6. 8 respectively, then the value of a^ 3 + b^ 3 is equal to

NTA Abhyas JEE Main 2020 Solution View → 148

Two data sets each of size 10 has the variance as 4 and k and the corresponding means as 2 and 4 respectively. If the variance of the combined data set is 5 ⋅ 5, then the value of

NTA Abhyas JEE Main 2020 Solution View → 149

If the variance of first n even natural numbers is 133 , then the value of n is equal to

NTA Abhyas JEE Main 2020 Solution View → 150

The mean of 40 observations is 20 and their standard deviation is 5 . If the sum of the squares of the observations is k , then the value of (k)/(1000) is

NTA Abhyas JEE Main 2020 Solution View → 151

In ten observations, the mean of all 10 numbers is 15 , the mean of the first six observations is 16 and the mean of the last five observations is 12 . The sixth number is

NTA Abhyas JEE Main 2020 Solution View → 152

In a factory, workers work in three shifts, say shift 1, shit 2 and shift 3 and they get wages in the ratio 3: 4: 8 depending on the shift 1, 2 and 3 respectively. Number of

NTA Abhyas JEE Main 2020 Solution View → 153

The mean and variance of 5 observations are 6 and 6.8 respectively. If a number equal to mean is included in the set of observations and the variance of 6 observations is k , then

NTA Abhyas JEE Main 2020 Solution View → 154

The mean deviation of the series a^ 2 , a^ 2 + d, a^ 2 + 2d,..... , a^ 2 + 2nd from its median is

NTA Abhyas JEE Main 2020 Solution View → 155

The average weight of students in a class of 35 students is 40kg . If the weight of the teacher is included, then the average rises by (1)/(3)kg . & The weight of the teacher is

NTA Abhyas JEE Main 2020 Solution View → 156

The mean of n observations is ¯ X . If the first observation is increased by 1 ^ 2 , second by 2 ^ 2 and so on, then the new mean is

NTA Abhyas JEE Main 2020 Solution View → 157

The mean of five observations is 4 and their variance is 2.8 . If three of these observations are 2, 2 and 5 , then the other two are

NTA Abhyas JEE Main 2020 Solution View → 158

If the standard deviation of n observations x _ 1 , x _ 2 ,..... , x _ n is 5 and for another set of n observations y _ 1 , y _ 2 ,..... , y _ n is 4, then the standard deviation

NTA Abhyas JEE Main 2020 Solution View → 159

If the mean of a set of observations x _ 1 , x _ 2 ,..... , x _ 10 is 40 , then the mean of x _ 1 + 4, x _ 2 + 8, x _ 3 + 12,.... , x _ 10 + 40 is

NTA Abhyas JEE Main 2020 Solution View → 160

If the variate of a distribution takes the values 1 ^ 2 , 2 ^ 2 , 3 ^ 2 ,... n^ 2 with frequencies n, n - 1, n - 2,... 3,2, 1 & respectively, then the mean value of the

NTA Abhyas JEE Main 2020 Solution View → 161

Let x _ 1 , x _ 2 ,.... , x _ n be n observations such that ∑ ( x _ i ) ^ 2 = 400 and ∑ x _ i = 40 , then a possible value of n among the following is

NTA Abhyas JEE Main 2020 Solution View → 162

If the mean of a set of observations x _ 1 , x _ 2 , x _ 3 ,.... , x _ n is &#175; x , then the mean of observations x _ i + 2i, ∀ i = 1,2, 3,.... n & is equal to

NTA Abhyas JEE Main 2020 Solution View → 163

Let x _ 1 , x _ 2 … , x _ n be n observations such that ∑ x _i^ 2 = 300 and ∑ x _ i = 90. Then a possible value of n among the following is

NTA Abhyas JEE Main 2020 Solution View → 164

The arithmetic mean of a set of 50 numbers is 38. If two numbers of the set, namely 60 and 40 are discarded, the arithmetic mean of the remaining set of numbers is

NTA Abhyas JEE Main 2020 Solution View → 165

Mean of the numbers 1,2, 3, … … … … , 9 with respective weights 1 ^ 2 + 1, 2 ^ 2 + 2, 3 ^ 2 + 3, … , 9 ^ 2 + 9 is

NTA Abhyas JEE Main 2020 Solution View → 166

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 2000 , then

JEE Main 2019 Solution View → 167

If both the mean 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

JEE Main 2019 Solution View → 168

If for some x ∈ R , the frequency distribution of the marks obtained by 20 students in a test is: Marks 2 3 5 7 Frequency distribution (x + 1) ^ 2 (2x - 5) x ^ 2 - 3x x Then the

JEE Main 2019 Solution View → 169

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 (y)/(x) is equal to:

JEE Main 2019 Solution View → 170

If the standard deviation of the numbers - 1,0, 1, k is 5 where k > 0, then k is equal to

JEE Main 2019 Solution View → 171

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

JEE Main 2019 Solution View → 172

The mean and variance for 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

JEE Main 2019 Solution View → 173

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

JEE Main 2019 Solution View → 174

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

JEE Main 2019 Solution View → 175

The outcome of each of 30 items was observed; 10 items gave an outcome (1)/(2)-d each, 10 items gave outcome (1)/(2) each and the remaining 10 items gave outcome (1)/(2)+d each.

JEE Main 2019 Solution View → 176

If the mean and standard deviation of 5 observations x _ 1 , x _ 2 , x _ 3 , x _ 4 , x _ 5 are 10 and 3, respectively, then the variance of 6 observations x _ 1 , x _ 2 , … , x _

JEE Main 2019 Solution View → 177

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

JEE Main 2019 Solution View → 178

A data consists of n observations: x _ 1 , x _ 2 , … , x _ n . If ∑ _ i = 1 ^ n ( x _ i + 1) ^ 2 = 9n and ∑ _ i = 1 ^ n ( x _ i - 1) ^ 2 = 5n , then the standard deviation of this

JEE Main 2019 Solution View → 179

5 students of a class have an average height 150cm and variance 18c m ^ 2 . A new student, whose height is 156cm, joined them. The variance (inc m ^ 2 ) of the height of these six

JEE Main 2019 Solution View → 180

The mean and the standard deviation (S . D .) of five observations are 9 and 0 , respectively. If one of the observation is increased such that the mean of the new set of five

JEE Main 2018 Solution View → 181

If the mean of the data: 7,8,9,7,8,7, λ, 8 is 8 , then the variance of this data is

JEE Main 2018 Solution View → 182

The mean of a set of 30 observations is 75 . If each other observation is multiplied by a nonzero number λ and then each of them is decreased by 25 , their mean remains the same.

JEE Main 2018 Solution View → 183

The mean of a set of 30 observation is 75 . If each observations is multiplied by non-zero number λ and then each of them is decreased by 25 , their mean remains the same. Then, λ

JEE Main 2018 Solution View → 184

If ∑ _ i = 1 ^ 9 ( x _ i - 5) = 9 and ∑ _ i = 1 ^ 9 ( x _ i - 5) ^ 2 = 45 , then the standard deviation of the 9 items x _ 1 , x _ 2 , … . , x _ 9 is

JEE Main 2018 Solution View → 185

The sum of 100 observations and the sum of their squares are 400 and 2475 , respectively. Later on, three observations 3, 4 and 5 were found to be incorrect. If the incorrect

JEE Main 2017 Solution View → 186

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

JEE Main 2017 Solution View → 187

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:

JEE Main 2017 Solution View → 188

The mean of 5 observations is 5 and their variance is 12 . 4 . If three of the observations are 1, 2 and 6 ; then the value of the remaining two is :

JEE Main 2016 Solution View → 189

If the mean deviation of the numbers 1, 1 + d, … , 1 + 100d from their mean is 255 , then a value of d is :

JEE Main 2016 Solution View → 190

If the standard deviation of the numbers 2, 3, a and 11 is 3 . 5 , then which of the following is true ?

JEE Main 2016 Solution View → 191

A factory is operating in two shifts, day and night, with 70 and 30 workers, respectively.If per day mean wage of the day shift workers is, ₹ 54 and per day mean wage of all the

JEE Main 2015 Solution View → 192

The mean of a data set comprising of 16 observations is 16 . If one of the observation value 16 is deleted and three new observations valued 3 , 4 and 5 are added to the data

JEE Main 2015 Solution View → 193

Let ¯ x , M and σ ^ 2 be respectively the mean, mode and variance of n observations x _ 1 , x _ 2 , . ... , x _ n and d _ i = - x _ i - a, i = 1, 2, . ... , n, where a is any

JEE Main 2014 Solution View → 194

Let X and M.D. be the mean and the mean deviation about X of n observations x_ i , i=1,2 ,n. If each of the observations is increased by 5 , then the new mean and the mean

JEE Main 2014 Solution View → 195

In a set of 2n distinct observations, each of the observation below the median of all the observations is increased by 5 and each of the remaining observations is decreased by 3 .

JEE Main 2014 Solution View → 196

The variance of the first 50 even natural numbers is :

JEE Main 2014 Solution View → 197

In a set of 2 n observations, half of them are equal to ' a ' and the remaining hall are equal to ' -a^ '. If the standard deviation of all the observations is 2 ; then the value

JEE Main 2013 Solution View → 198

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

JEE Main 2013 Solution View → 199

Mean of 5 observations is 7 . If four of these observations are 6,7,8,10 and one is missing then the variance of all the five observations is :

JEE Main 2013 Solution View → 200

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:

JEE Main 2013 Solution View →
Practice all Statistics questions in the app →

Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)

Statistics in other exams

NDA Statistics (236)BITSAT Statistics (19)