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?

**[2002]**

**Option A**: 73

**Option B**: 65

**Option C**: 68

**Option D**: 74

**Show/Hide Answer Key**

**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

**[2002]**

**Option A**: 8 / 3

**Option B**: 3 / 8

**Option C**: 4 / 5

**Option D**: 5 / 4

**Show/Hide Answer Key**

**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

**[2003]**

**Option A**: 8.33

**Option B**: 78.00

**Option C**: 188.66

**Option D**: 177.33

**Show/Hide Answer Key**

**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

**[2003]**

**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

**Show/Hide Answer Key**

**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?

**[2004]**

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

**Option B**: Only (B)

**Option C**: Only (A) and (B)

**Option D**: Only (A)

**Show/Hide Answer Key**

**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.

**[2004]**

**Option A**: (√2 / n)

**Option B**: √2

**Option C**: 2

**Option D**: (1 / n)

**Show/Hide Answer Key**

**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

**[2004]**

**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)

**Show/Hide Answer Key**

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

**Statistics Questions and Answers No:8**

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

**[2005]**

**Option A**: 22.0

**Option B**: 20.5

**Option C**: 25.5

**Option D**: 24.0

**Show/Hide Answer Key**

**Option D: 24.0**

**Statistics Questions with Solutions No: 9**

Let x_{1}, x_{2}…….. x_{n} be n observations such that = 400 and x_{i} = 80. Then the possible value of n among the following is

**[2005]**

**Option A**: 15

**Option B**: 18

**Option C**: 9

**Option D**: 12

**Show/Hide Answer Key**

**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

**[2005]**

**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

**Show/Hide Answer Key**

**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 V_{A} and V_{B} represent the variances of the two populations, respectively then (V_{A }/ V_{B}) is

**[2006]**

**Option A**: 1

**Option B**: 9 / 4

**Option C**: 4 / 9

**Option D**: 2 / 3

**Show/Hide Answer Key**

**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

**[2006]**

**Option A**: (3 / 2) x^{2}

**Option B**: (√x^{3 }/ √ 8)

**Option C**: (1 / 2) x^{2}

**Option D**: πx^{2}

**Show/Hide Answer Key**

**Option C: (1 / 2) x ^{2}**

**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

**[2007]**

**Option A**: 80

**Option B**: 60

**Option C**: 40

**Option D**: 20

**Show/Hide Answer Key**

**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?

**[2008]**

**Option A**: a = 0, b = 7

**Option B**: a = 5, b = 2

**Option C**: a = 1, b = 6

**Option D**: a = 3, b = 4

**Show/Hide Answer Key**

**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:

**[2009]**

**Option A**: 20.0

**Option B**: 10.1

**Option C**: 20.2

**Option D**: 10.0

**Show/Hide Answer Key**

**Option B: 10.1**

**Statistics Problems for Class 12 JEE Questions No: 16**

Statement I : The variance of first n even natural numbers is (n^{2 }– 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 )

**[2009]**

**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

**Show/Hide Answer Key**

**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

**[2010]**

**Option A**: 11 / 2

**Option B**: 6

**Option C**: 13 / 2

**Option D**: 5 / 2

**Show/Hide Answer Key**

**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

**[2011]**

**Option A**: 3

**Option B**: 4

**Option C**: 5

**Option D**: 2

**Show/Hide Answer Key**

**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

**[2011]**

**Option A**: (32, 2)

**Option B**: (32, 4)

**Option C**: (28, 2)

**Option D**: (28, 4)

**Show/Hide Answer Key**

**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

**[2012]**

**Option A**: 8

**Option B**: 5

**Option C**: 1

**Option D**: 3

**Show/Hide Answer Key**

**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 )

**[2012]**

**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

**Show/Hide Answer Key**

**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

**[2012]**

**Option A**: 34

**Option B**: 31

**Option C**: 26

**Option D**: 36

**Show/Hide Answer Key**

**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

**[2012]**

**Option A**: 10

**Option B**: 20

**Option C**: 15

**Option D**: 12

**Show/Hide Answer Key**

**Option A: 10**

**Statistics Questions and Answers No:24**

Let X_{1}, X_{2},…… X_{n }be n observations, and let **x** be their arithmetic mean and σ^{2} be their variance. Statement I : Variance of 2x_{1}, 2x_{2}…… 2x^{n} is 4σ².

Statement II : Arithmetic mean of 2x_{1}. 2x_{2}…. 2x_{n}, is 4x.

**[2012]**

**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

**Show/Hide Answer Key**

**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:

**[2013]**

**Option A**: 2

**Option B**: √2

**Option C**: 4

**Option D**: 2√2

**Show/Hide Answer Key**

**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 ?

**[2013]**

**Option A**: Mean

**Option B**: Median

**Option C**: Mode

**Option D**: Variance

**Show/Hide Answer Key**

**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

**[2013]**

**Option A**: 41

**Option B**: 49

**Option C**: 40.5

**Option D**: 42.5

**Show/Hide Answer Key**

**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:

**[2013]**

**Option A**: 18

**Option B**: 10

**Option C**: 5

**Option D**: 14

**Show/Hide Answer Key**

**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 x_{i} = 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

**[2014]**

**Option A**: **X****, **M.D.

**Option B**: **X**** **+ 5, M.D.

**Option C**: **X****, **M.D.+ 5

**Option D**: **X**** **+ 5, M.D. + 5

**Show/Hide Answer Key**

**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 x_{1}, x_{2}, ……. x_{n} and d_{i} = -x_{i }– a, i = 1, 2,…..n, where a is any number.

Statement I: Variance of d_{1}, d_{2}…. d is σ².

Statement II: Mean and mode of d_{₁}, d_{2}….. d_{n} are –**x**** **– a and -M – a, respectively.

**[2014]**

**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

**Show/Hide Answer Key**

**Option B: Statement I and Statement II are both true
**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |