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# JEE Main Math Previous Year Papers Statistics Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Math Previous Year Paper Statistics Questions Answer Keys Solutions.

### JEE Mains Mathematics Statistics Questions Bank

JEE Statistics Questions No:1

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?



Option A: 73

Option B: 65

Option C: 68

Option D: 74

Option B: 65

JEE Main Statistics Questions No:2

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is



Option A: 8 / 3

Option B: 3 / 8

Option C: 4 / 5

Option D: 5 / 4

Option D: 5 / 4

JEE Mathematics Statistics Questions No: 3

In an experiment with 15 observations on x, the following results were available: Σx² = 2830, Σx = 170 One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is



Option A: 8.33

Option B: 78.00

Option C: 188.66

Option D: 177.33

Option B: 78.00

JEE Main Math Statistics Questions No:4

The median of a set of 9 distinct observations is 20.5, If each of the largest 4 observations of the set is increased by 2, then the median of the new set



Option A: Remains the same as that of the original set

Option B: Is increased by 2

Option C: Is decreased by 2

Option D: Is two times the original median

Option A: Remains the same as that of the original set

Statistics JEE Questions No:5

Consider the following statements :

(A) Mode can be computed from histogram

(B) Median is not independent of change of scale

(C) Variance is independent of change of origin and scale.

Which of these is/ are correct?



Option A: (A), (B) and (C)

Option B: Only (B)

Option C: Only (A) and (B)

Option D: Only (A)

Option C:  Only (A) and (B)

Statistics JEE Main Questions No:6

In a series of 2 n observations, half of them equal a and remaining half equal -a. If the standard deviation of the observations is 2, then | a | equals.



Option A: (√2 / n)

Option B: √2

Option C: 2

Option D: (1 / n)

Option C: 2

Statistics Questions for JEE Mains Questions No:7

Three forces P, Q and R acting along IA, IB and IC, where I is the incentre of a △ABC, are in equilibrium. Then P : Q : R is



Option A: cos (A / 2) : cos (B / 2) : cos (C / 2)

Option B: sin (A / 2) : sin (B / 2) : sin (C / 2)

Option C: sec (A / 2) : sec (B / 2) : sec (C / 2)

Option D: cosec (A / 2) : co sec (B / 2) : co sec (C / 2)

Option A: cos (A / 2) : cos (B / 2) ; cos (C / 2)

If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately



Option A: 22.0

Option B: 20.5

Option C: 25.5

Option D: 24.0

Option D: 24.0

Statistics Questions with Solutions No: 9

Let x1, x2…….. xn be n observations such that = 400 and xi = 80. Then the possible value of n among the following is



Option A: 15

Option B: 18

Option C: 9

Option D: 12

Option B: 18

JEE Mains Statistics Questions No:10

ABC is a triangle. Forces P, Q, R acting along IA, IB and IC respectively are in equilibrium, where I is the incentre of △ABC. Then P : Q : R is



Option A: sin A : sin B : sin C

Option B: sin (A / 2) : sin (B / 2) : sin (C / 2)

Option C: cos (A / 2) : cos (B / 2) : cos (C / 2)

Option D: cos A  : cos B : cos C

Option C: cos (A / 2) : cos (B / 2) : cos (C / 2)

JEE Mains Math Statistics Questions No: 11

Suppose a population A has 100 observations 101, 102,……….. 200 and another population B has 100 observations 151, 152, ……………250. If VA and VB represent the variances of the two populations, respectively then (VA / VB) is



Option A: 1

Option B: 9 / 4

Option C:  4 / 9

Option D: 2 / 3

Option A: 1

Statistics Questions for JEE Questions No: 12

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park



Option A: (3 / 2) x2

Option B: (√x3  / √ 8)

Option C: (1 / 2) x2

Option D: πx2

Option C:  (1 / 2) x2

Statistics Problems for Class 11 Questions No: 13

The average marks of boys in class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is



Option A: 80

Option B: 60

Option C: 40

Option D: 20

Option A: 80

Statistics Problems for Class 12 Questions No: 14

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?



Option A: a = 0, b = 7

Option B: a = 5,  b = 2

Option C: a = 1,  b = 6

Option D: a = 3,  b = 4

Option D: a = 3,  b = 4

Statistics Problems for Class 11 JEE Questions No: 15

If the mean deviation of the numbers 1, 1 + d, 1 + 2d,…. 1 + 100d from their mean is 255, then d is equal to:



Option A: 20.0

Option B: 10.1

Option C: 20.2

Option D: 10.0

Option B: 10.1

Statistics Problems for Class 12 JEE Questions No: 16

Statement I : The variance of first n even natural numbers is (n2 – 1 / 4)

Statement-II: The sum of first n natural numbers is n (n + 1) / 2 and the sum of squares of first n  natural numbers is (n (n + 1) (2n + 1) / 6 )



Option A: Statement I is True; Statement II is true: Statement II is not a correct explanation for Statement I

Option B: Statement I is True; Statement  Il is False.

Option C: Statement I is False; Statement II is True

Option D: Statement I is True; Statement  II is True; Statement II is a correct explanation for

Option C: A Statement I is False; Statement II is True

JEE Statistics Questions No:17

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is



Option A: 11 / 2

Option B: 6

Option C: 13 / 2

Option D: 5 / 2

Option A: 11 / 2

JEE Main Statistics Questions No:18

If the mean deviation about the median of the numbers a, 2a,………50a is 50, then | a | equals



Option A: 3

Option B: 4

Option C: 5

Option D: 2

Option B:  4

JEE Mathematics Statistics Questions No:19

A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standarion deviation of 2 gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (in gm) of fishes are respectively



Option A: (32, 2)

Option B: (32, 4)

Option C: (28, 2)

Option D: (28, 4)

Option A: (32, 2)

JEE Main Math Statistics Questions No:20

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



Option A: 8

Option B: 5

Option C: 1

Option D: 3

Option D:  3

Statistics JEE Questions No:21

Statement 1: The variance of first n odd natural numbers is ( (n² – 1) / 3 )

Statement 2: The sum of first n odd natural number is n² and the sum of square of first n odd natural numbers is ( n (4n² + 1) / 3 )



Option A: Statement 1 is true, Statement 2 is false

Option B: Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1

Option C: Statement 1 is false, Statement 2 is true

Option D: Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1

Option A: Statement 1 is true, Statement 2 is false.

Statistics JEE Main Questions No:22

The frequency distribution of daily working expenditure of families in a locality is as follows: If the mode of the distribution is ₹140, then the value of b



Option A: 34

Option B: 31

Option C: 26

Option D: 36

Option D: 36

Statistics Questions for JEE Mains Questions No:23

The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 – 30 and the number of observations less than 20 is 45, then the frequency of median class is



Option A: 10

Option B: 20

Option C: 15

Option D: 12

Option A: 10

Let X1, X2,…… Xn be n observations, and let x be their arithmetic mean and σ2 be their variance. Statement I : Variance of 2x1, 2x2…… 2xn is 4σ².

Statement II : Arithmetic mean of 2x1. 2x2…. 2xn, is 4x.



Option A: Statement I is True; Statement II is true; Statement  Il is not a correct explanation for Statement I

Option B: Statement I is True; Statement  II is False.

Option C: Statement I is False; Statement II is True.

Option D: Statement I is True; Statement Il is True; Statement II is a correct explanation for Statement I

Option B: Statement I is True; Statement  II is False.

Statistics Questions with Solutions No:25

In a set of 2n observations, half of them are equal to ‘a’ and the remaining half are equal to ‘-a’. If the standard deviation of all the observations is 2; then the value of | a | is:



Option A: 2

Option B: √2

Option C: 4

Option D: 2√2

Option A: 2

JEE Mains Statistics Questions No:26

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 ?



Option A: Mean

Option B: Median

Option C: Mode

Option D: Variance

Option D: Variance

JEE Mains Math Statistics Questions No: 27

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



Option A: 41

Option B: 49

Option C: 40.5

Option D: 42.5

Option A: 41

Statistics Questions for JEE Questions No: 28

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:



Option A: 18

Option B: 10

Option C: 5

Option D: 14

Option D: 14

Statistics Problems for Class 11 Questions No: 29

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



Option A: X, M.D.

Option B: X + 5, M.D.

Option C: X, M.D.+ 5

Option D: X + 5, M.D. + 5

Option B: X + 5, M.D.

Statistics Problems for Class 12 Questions No: 30

Let x, M and σ² be respectively the mean, mode and variance of n observations x1, x2, ……. xn and di = -xi – a, i = 1, 2,…..n, where a is any number.

Statement I: Variance of d1, d2…. d is σ².

Statement II: Mean and mode of d, d2….. dn are –x – a and -M – a, respectively.



Option A: Statement I and Statement II are both false

Option B: Statement I and Statement II are both true

Option C: Statement I is true and Statement II is false

Option D: Statement I is false and Statement II is true