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 Mathematics Previous Paper Statistics Questions Answer Keys Solutions*.

### JEE Mains Mathematics Statistics Questions Bank

**Statistics Problems for Class 11 JEE Questions No: 31**

The variance of first 50 even natural numbers is

**[2014]**

**Option A**: 437

**Option B**: 437 / 4

**Option C**: 833 / 4

**Option D**: 833

**Show/Hide Answer Key**

**Option D: 833**

**Statistics Problems for Class 12 JEE Questions No: 32**

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

**[2014]**

**Option A**: Increases by 1

**Option B**: Decreases by 1

**Option C**: Decreases by 2

**Option D**: Increases by 2

**Show/Hide Answer Key**

**Option A: Increases by 1**

**JEE Statistics Questions No:33**

The locus of the center of a circle which touches the circle |z – z_{1}| = a and |z – z_{2}| = b externally (z, z_{1}, z_{2} are complex numbers) will be

**[2014]**

**Option A**: An Ellipse

**Option B**: A Hyperbola

**Option C**: A Circle

**Option D**: None of These

**Show/Hide Answer Key**

**Option B: A Hyperbola**

**JEE Main Statistics Questions No:34**

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 workers is ₹60, then per day mean wage of the night shift workers (in ₹) is

**[2014]**

**Option A**: 69

**Option B**: 66

**Option C**: 74

**Option D**: 75

**Show/Hide Answer Key**

**Option C: 74**

**JEE Mathematics Statistics Questions No:35**

Let the sum of the first three terms of an A.P, be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is:

**[2015]**

**Option A**: 28

**Option B**: 26.5

**Option C**: 29.5

**Option D**: 31

**Show/Hide Answer Key**

**Option C: 29.5**

**JEE Main Math Statistics Questions No:36**

The mean of the 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, then the mean of the resultant data, is:

**[2015]**

**Option A**: 15.8

**Option B**: 14.0

**Option C**: 16.8

**Option D**: 16.0

**Show/Hide Answer Key**

**Option B: 14.0**

**Statistics JEE Questions No:37**

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

**[2016]**

**Option A**: 10.1

**Option B**: 5.05

**Option C**: 20.2

**Option D**: 10

**Show/Hide Answer Key**

**Option A: 10.1**

**Statistics JEE Main Questions No:38**

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

**[2016]**

**Option A**: 3a^{2 –} 34a + 91 = 0

**Option B**: 3a^{2 –} 23a + 44 = 0

**Option C**: 3a^{2 –} 26a + 55 = 0

**Option D**: 3a^{2 –} 32a + 84 = 0

**Show/Hide Answer Key**

**Option D: 3a² – 32a + 84 = 0**

**Statistics Questions for JEE Mains Questions No:39**

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 observations are omitted, then the variance of the remaining observations is :

**[2017]**

**Option A**: 8.25

**Option B**: 8.50

**Option C**: 8.00

**Option D**: 9.00

**Show/Hide Answer Key**

**Option D: 9.00**

**Statistics Questions and Answers No:40**

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 now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is

**[2017]**

**Option A**: 25

**Option B**: 30

**Option C**: 35

**Option D**: 40

**Show/Hide Answer Key**

**Option C: 35**

**Statistics Questions with Solutions No:41**

If

_{i }– 5) = 9 and (x

_{i }– 5)

^{2}= 45, then the standard deviation of the 9 items x

_{1}, x

_{2},……… x

_{9}is:

**[2018]**

**Option A**: 4

**Option B**: 2

**Option C**: 3

**Option D**: 9

**Show/Hide Answer Key**

**Option B: 2**

**JEE Mains Statistics Questions No:42**

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

**[2018]**

**Option A**: 9 / 8

**Option B**: 2

**Option C**: 7 / 8

**Option D**: 1

**Show/Hide Answer Key**

**Option D: 1**

**JEE Mains Math Statistics Questions No: 43**

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

**[2018]**

**Option A**: 10 / 3

**Option B**: 4 / 3

**Option C**: 1 / 3

**Option D**: 2 / 3

**Show/Hide Answer Key**

**Option B: 4 / 3**

**Statistics Questions for JEE Questions No: 44**

5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is:

**[2019]**

**Option A**: 16

**Option B**: 22

**Option C**: 20

**Option D**: 18

**Show/Hide Answer Key**

**Option C: 20**

**Statistics Problems for Class 11 Questions No: 45**

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:

**[2019]**

**Option A**:10 : 3

**Option B**: 4 : 9

**Option C**: 5 : 8

**Option D**: 6 : 7

**Show/Hide Answer Key**

**Option B: 4 : 9**

**Statistics Problems for Class 12 Questions No: 46**

A data consists of n observations: x_{1,} x_{2}…..x_{n} . If (x_{i} + 1)² = 9n and (x_{i}-1)² = 5n then the standard deviation of this data is:

**[2019]**

**Option A**: 2

**Option B**: √5

**Option C**: 5

**Option D**: √7

**Show/Hide Answer Key**

**Option B: √5**

**Statistics Problems for Class 11 JEE Questions No: 47**

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. 2 If the variance of this outcome data is (4/3) then | d | equals:

**[2019]**

**Option A**: (2 / 3)

**Option B**: 2

**Option C**: (√5 / 2)

**Option D**: √2

**Show/Hide Answer Key**

**Option D: √2**

**Statistics Problems for Class 12 JEE Questions No: 48**

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

**[2019]**

**Option A**: 30

**Option B**: 51

**Option C**: 50

**Option D**: 31

**Show/Hide Answer Key**

**Option D: 31**

**JEE Statistics Questions No:49**

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 deviation of the marks in six tests is:

**[2019]**

**Option A**: (10 / √3)

**Option B**: (100 / 3)

**Option C**: (10 / 3)

**Option D**: (100 / √3)

**Show/Hide Answer Key**

**Option A: (10 / √3)**

**JEE Main Statistics Questions No:50**

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

**[2019]**

**Option A**: 2√6

**Option B**: 2 (√10 / √3)

**Option C**: 4 (√5 / √3)

**Option D**: √6

**Show/Hide Answer Key**

**Option A: 2√6 **

**JEE Mathematics Statistics Questions No:51**

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 }– 4)^{2} is

**[2019]**

**Option A**: 400

**Option B**: 380

**Option C**: 525

**Option D**: 480

**Show/Hide Answer Key**

**Option A: 400**

**JEE Main Math Statistics Questions No:52**

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 :

**[2019]**

**Option A**: 2√2

**Option B**: 2

**Option C**: 4

**Option D**: √2

**Show/Hide Answer Key**

**Option B: 2**

**Statistics JEE Questions No:53**

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

**[2019]**

**Option A**: 9 / 4

**Option B**: 7 / 2

**Option C**: 8 / 3

**Option D**: 7 / 3

**Show/Hide Answer Key**

**Option D: 7 / 3**

**Statistics JEE Main Questions No:54**

If for some x € **R**, the frequency distribution of the marks obtained by 20 students in a test is :

then the mean of the marks is:

**[2019]**

**Option A**: 3.2

**Option B**: 3.0

**Option C**: 2.5

**Option D**: 2.8

**Show/Hide Answer Key**

**Option D: 2.8**

**Statistics Questions for JEE Mains Questions No:55**

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

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 18**

**Statistics Questions and Answers No:56**

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 ≠ 0. If the new mean and new s.d. become half of their original values, then q is equal to:

**[2020]**

**Option A**: -5

**Option B**: 10

**Option C**: -20

**Option D**: -10

**Show/Hide Answer Key**

**Option C: -20**

**Statistics Questions with Solutions No:57**

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

**[2020]**

**Show/Hide Answer Key**

**Correct Ans: 3**

**JEE Mains Statistics Questions No:58**

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

**[2020]**

**Option A**: 7

**Option B**: -7

**Option C**: -27

**Option D**: 9

**Show/Hide Answer Key**

**Option B: -7**

**JEE Mains Math Statistics Questions No: 59**

Let x_{i }(1 ≤ i ≤ 10) be ten observations of a random variable X. If (x_{i }– p) = 3 and (x_{i }– p)^{2} = 9 where 0 ≠ p ϵ R, then the standard deviation of these observations is

**[2020]**

**Option A**: (√3 / √5)

**Option B**: (4 / 5)

**Option C**: (9 / 10)

**Option D**: (7 /10)

**Show/Hide Answer Key**

**Option C: (9 / 10)**

**Statistics Questions for JEE Questions No: 60**

For the frequency distribution:

where 0 < x_{1} < x_{2 }< x_{3} < …..< x_{15 }= 10 and f_{i} > 0, the standard deviation cannot be:

**[2020]**

**Option A**: 4

**Option B**: 1

**Option C**: 6

**Option D**: 2

**Show/Hide Answer Key**

**Option C: 6**

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 | |