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Statistics — NDA Mathematics PYQs

236 previous year questions from Statistics with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

236 questionsMathematicsSolutions on every page
1

Let two lines of regression be x+y+11=0 and 2x+3y+4=0 for some data. What is the value of correlation coefficient between x and y ?

NDA 2026 Solution View → 2

Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : Marks 0 - 10 10 - 20 20 - 30 30 - 40 No. of students 10 20 f 40 Question

NDA 2026 Solution View → 3

The standard deviation of 100 observations is 10 . If 5 is multiplied to each of the observations, then what is the new standard deviation ?

NDA 2026 Solution View → 4

Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : Marks 0 - 10 10 - 20 20 - 30 30 - 40 No. of students 10 20 f 40 Question

NDA 2026 Solution View → 5

If the mean of 20 observations, namely x₁,x₂,x₃, ,x₂₀ is 1 414 , then what is the value of _ i=1 ²⁰100(2x_i+4) ?

NDA 2026 Solution View → 6

If the random variable X has mean 3 and standard deviation 5 , then what is the variance of the random variable Y=2X-5 ?

NDA 2026 Solution View → 7

The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard deviation?

NDA 2025 Solution View → 8

Consider the following statements: I. Mean and variance have the same unit of measurement. II. Mean deviation and standard deviation have the same unit of measurement. Which of the

NDA 2025 Solution View → 9

Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Height (in cm) Number of Students 160–162 12

NDA 2025 Solution View → 10

Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Height (in cm) Number of Students 160–162 12

NDA 2025 Solution View → 11

Consider the following for the two (02) items that follow: The sum and the sum of squares of the observations corresponding to length X (in cm) and weight Y (in gm) of 50 tropical

NDA 2025 Solution View → 12

The arithmetic mean of 100 observations is 50. If 5 is subtracted from each observation and then divided by 20, then what is the new arithmetic mean?

NDA 2025 Solution View → 13

The standard deviation of 100 observations is 10. If 5 is added to each observation and then divided by 20, then what will be the new standard deviation?

NDA 2025 Solution View → 14

Consider the following for the two (02) items that follow: The sum and the sum of squares of the observations corresponding to length X (in cm) and weight Y (in gm) of 50 tropical

NDA 2025 Solution View → 15

Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Height (in cm) Number of Students 160–162 12

NDA 2025 Solution View → 16

The frequency distribution of the marks obtained by students in a Science examination is given below: Marks 5–15 15–25 25–35 35–45 Number of students 20 30 30 20 What is the arithm

NDA 2025 Solution View → 17

What is the arithmetic mean of 8^2 , 9^2 , 10^2 , , 15^2 ?

NDA 2025 Solution View → 18

Consider the following for the four (04) items that follow: The frequency distribution of height of students of a class is given below: Height (in cm) Number of Students 160–162 12

NDA 2025 Solution View → 19

What is the mean deviation of the first 10 natural numbers?

NDA 2024 Solution View → 20

Let _ i=1 ^9 x_i^2=855 . If M is the mean and is the standard deviation of x₁, x₂, . . x₉ , then what is the value of M ^2+ ^2 ?

NDA 2024 Solution View → 21

The mean of the series x₁, x₂, , x_n is x . If x_n is replaced by k , then what is the new mean?

NDA 2024 Solution View → 22

From data (-4,1),(-1,2),(2,7) and (3,1) , the regression line of y on x is obtained as y=a+b x , then what is the value of 2 a+15 b ?

NDA 2024 Solution View → 23

The marks obtained by 10 students in a Statistics test are 24,47,18,32,19,15,21,35,50 and 41. What is the variance of the largest five observations?

NDA 2024 Solution View → 24

array |c|c|c|c|c|c| _i & 1 & 2 & 3 & & n _i & 1 & 2⁻¹ & 2⁻² & & 2^ -(n-1) array What is the mean of the distribution?

NDA 2024 Solution View → 25

The marks obtained by 10 students in a Statistics test are 24,47,18,32,19,15,21,35,50 and 41. What is the mean deviation of the largest five observations?

NDA 2024 Solution View → 26

The sum of deviations of n numbers from 10 and 20 are p and q respectively. If (p-q)^2=10000 , then what is the value of n ?

NDA 2023 Solution View → 27

If X =20 is the mean of 10 observations x₁, x₂ , x₁₀ , then what is the value of _ i=1 ¹⁰ ( 3 x_i-4 5 ) ?

NDA 2023 Solution View → 28

If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

NDA 2023 Solution View → 29

If r is the coefficient of correlation between x and y , then what is the correlation coefficient between (3 x+4) and (-3 y+3) ?

NDA 2023 Solution View → 30

The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11,16 and 20. What are the other two observations?

NDA 2023 Solution View → 31

The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9 p=3 q=2 r=6 s . What is the value of 4 p-q ?

NDA 2023 Solution View → 32

The observations 4,1,4,3,6,2,1,3,4,5,1,6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then

NDA 2023 Solution View → 33

The bivariate data set contains only two points (-1,1) and ( 3,2 ) What will be the line of regression of y on x ?

NDA 2023 Solution View → 34

A die is thrown 10 times and obtained the following outputs: 1,2,1,1,2,1,4,6,5,4 What will be the mode of data so obtained?

NDA 2023 Solution View → 35

Consider the following frequency distribution: What is the value of median of the distribution?

NDA 2023 Solution View → 36

Let P, Q, R represent mean, median and mode. If for some distribution 5 P=4 Q= R 2 , then what is P+Q 2 P+0.7 R equal to?

NDA 2023 Solution View → 37

For data -1,1,4,3,8,12,17,19,9,11 ; if M is the median of first 5 observations and N is the median of last five observations then what is the value of 4 M-N ?

NDA 2023 Solution View → 38

Let P be the median, Q be the mean and R be the mode of observations x₁, x₂, x₃, x n . Let S= _ i=1 ^n (2 x_i-a )^2 . S takes minimum value, when a is equal to

NDA 2023 Solution View → 39

The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below: array |c|c|c|c|c| Subject & Mathematics & Physics & Chemistry & Biol

NDA 2022 Solution View → 40

The coefficient of correlation between ages of husband and wife at the time of marriage for a given set of 100 couples was noted to be 0 7 . Assume that all these couples survive t

NDA 2022 Solution View → 41

Consider the following grouped frequency distribution : array |l|l|l|l|l|l|l| Class & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 Frequency & 1 & 2 & 4 & 6 & 4 & 3 array What is m

NDA 2022 Solution View → 42

Consider the following grouped frequency distribution : array |l|l|l|l|l|l|l| Class & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 Frequency & 1 & 2 & 4 & 6 & 4 & 3 array What is t

NDA 2022 Solution View → 43

The frequency curve (assuming unimodal) corresponding to the data obtained in an experiment is skewed to the left. What conclusion can be drawn from the curve?

NDA 2022 Solution View → 44

Consider the following grouped frequency distribution : array |l|l|l|l|l|l|l| Class & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 Frequency & 1 & 2 & 4 & 6 & 4 & 3 array What is t

NDA 2022 Solution View → 45

The algebraic sum of the deviations of a set of values x₁ , x₂, x₃, x_n measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92

NDA 2022 Solution View → 46

The variance of five positive observations is 3.6. If four of the observations are 2,2,4,5 then what is the remaining observation?

NDA 2022 Solution View → 47

array |c|c|c|c|c|c| Class & 0-20 & 20-40 & 40-60 & 60-80 & 80-100 Frequency & 17 & p+q & 32 & p-3 q & 19 array The total frequency is 120 . The mean is 50 . What is the value of q

NDA 2022 Solution View → 48

The algebraic sum of the deviations of a set of values x₁ , x₂, x₃, x_n measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92

NDA 2022 Solution View → 49

array |c|c|c|c|c|c| Class & 0-20 & 20-40 & 40-60 & 60-80 & 80-100 Frequency & 17 & p+q & 32 & p-3 q & 19 array The total frequency is 120 . The mean is 50 . If the frequency of eac

NDA 2022 Solution View → 50

The mean and standard deviation (SD) of marks obtained by 50 students of a class in 4 subjects are given below: array |c|c|c|c|c| Subject & Mathematics & Physics & Chemistry & Biol

NDA 2022 Solution View → 51

What is the coefficient of mean deviation of 21,34,23,39 , 26,37,40,20,33,27 (taken from mean)?

NDA 2022 Solution View → 52

The algebraic sum of the deviations of a set of values x₁ , x₂, x₃, x_n measured from 100 is -20 and the algebriac sum of the deviations of the same set of values measured from 92

NDA 2022 Solution View → 53

array |c|c|c|c|c|c| Class & 0-20 & 20-40 & 40-60 & 60-80 & 80-100 Frequency & 17 & p+q & 32 & p-3 q & 19 array The total frequency is 120 . The mean is 50 . What is the value of p

NDA 2022 Solution View → 54

Two regression lines are given as 3 x-4 y+8=0 and 4 x-3 y-1=0 . Consider the following statements : 1. The coefficient of correlations r is 3 4 . 2. The means of x and y are 3 and

NDA 2021 Solution View → 55

The marks obtained by 60 students in a certain subject out of 75 are given below : array |cc| Marks & Number of Students 15-20 & 4 20-25 & 5 25-30 & 11 30-35 & 6 35-40 & 5 40-45 &

NDA 2021 Solution View → 56

For the set of numbers x, x, x+2, x+3, x+10 where x is a natural number, which of the following is/are correct? 1. Mean Mode 2. Median Mean Select the correct answer using the code

NDA 2021 Solution View → 57

The marks obtained by 60 students in a certain subject out of 75 are given below : array |cc| Marks & Number of Students 15-20 & 4 20-25 & 5 25-30 & 11 30-35 & 6 35-40 & 5 40-45 &

NDA 2021 Solution View → 58

The mean of 10 observations is 5.5 . If each observation is multiplied by 4 and subtracted from 44 , then what is the new mean?

NDA 2021 Solution View → 59

Consider the following measures of central tendency for a set of N numbers : 1. Arithmetic mean 2. Geometric mean Which of the above uses/use all the data?

NDA 2021 Solution View → 60

For a histogram based on a frequency distribution with unequal class intervals, the frequency of a class should be proportional to

NDA 2021 Solution View → 61

What is the mean deviation of first 10 even natural numbers?

NDA 2021 Solution View → 62

The coefficient of correlation is independent of

NDA 2021 Solution View → 63

The numbers of Science, Arts and Commerce graduates working in a company are 30,70 and 50 respectively. If these figures are represented by a pie chart, then what is the angle corr

NDA 2021 Solution View → 64

The following table gives the frequency distribution of number of peas per pea pod of 198 pods : What is the median of this distribution?

NDA 2021 Solution View → 65

If M is the mean of n observations x₁-k, x₂-k, x₃-k , , x_n-k , where k is any real number, then what is the mean of x₁, x₂, x₃, , x_n ?

NDA 2021 Solution View → 66

For which of the following sets of numbers do the mean, median and mode have the same value?

NDA 2021 Solution View → 67

If the mean of a frequency distribution is 100 and the coefficient of variation is 45 % , then what is the value of the variance?

NDA 2021 Solution View → 68

What is the sum of deviations of the variate values 73 , 85,92,105,120 from their mean?

NDA 2021 Solution View → 69

If _ i=1 ¹⁰ x_i=110 and _ i=1 ¹⁰ x_i^2=1540 then what is the variance?

NDA 2021 Solution View → 70

When the measure of central tendency is available in the form of mean, which one of the following is the most reliable and accurate measure of variability?

NDA 2021 Solution View → 71

The mean of 12 observations is 75 . If two observations are discarded, then the mean of the remaining observations is 65 . What is the mean of the discarded observations?

NDA 2021 Solution View → 72

If the mode of the scores 10,12,13,15,15,13,12,10, x is 15 , then what is the value of x ?

NDA 2021 Solution View → 73

The average of a set of 15 observations is recorded, but later it is found that for one observation, the digit in the tens place was wrongly recorded as 8 instead of 3 . After corr

NDA 2021 Solution View → 74

Paragraph: Read the following information and answer: Consider the following statements : 1. Modal value of the marks in Physics lies in the interval 30-40 . 2. Median of the marks

NDA 2020 Solution View → 75

Paragraph: Read the following information and answer: What is the mean of marks in Physics?

NDA 2020 Solution View → 76

The arithmetic mean of 100 observations is 40 . Later, it was found that an observation '53' was wrongly read as ' 83 '. What is the correct arithmetic mean?

NDA 2020 Solution View → 77

A data set of n observations has mean 2 M , while another data set of 2 n observations has mean M . What is the mean of the combined data sets?

NDA 2020 Solution View → 78

The sum of deviations of n number of observations measured from 2.5 is 50 . The sum of deviations of the same set of observations measured from 3.5 is -50 . What is the value of n

NDA 2020 Solution View → 79

Paragraph: Read the following information and answer: The difference between number of students under Physics and Mathematics is largest for the interval

NDA 2020 Solution View → 80

The numbers 4 and 9 have frequencies x and (x-1) respectively. If their arithmetic mean is 6 , then what is the value of x ?

NDA 2020 Solution View → 81

If x_i=20, x_i^2=200 and n=10 for an observed variable x , then what is the coefficient of variation?

NDA 2020 Solution View → 82

Let X and Y represent prices (in ₹) of a commodity in Kolkata and Mumbai respectively. It is given that X=65, Y=67 , _X=2.5, _Y=3.5 and r(X, Y)=0.8 . What is the equation of regres

NDA 2020 Solution View → 83

What is the standard deviation of the observations - 6 ,- 5 ,- 4 ,-1,1, 4 , 5 , 6 ?

NDA 2020 Solution View → 84

The median of the observations 22,24,33,37, x+1, x+3,46 , 47,57,58 in ascending order is 42 . What are the values of 5 th and 6 th observations respectively?

NDA 2019 Solution View → 85

Arithmetic mean of 10 observations is 60 and sum of squares of deviations from 50 is 5000 . What is the standard deviation of the observations?

NDA 2019 Solution View → 86

For the variables x and y , the two regression lines are 6 x+y=30 and 3 x+2 y=25 . What are the values of x , y and r respectively?

NDA 2019 Solution View → 87

The class marks in a frequency table are given to be 5,10 , 15,20,25,30,35,40,45,50 . The class limits of the first five classes are

NDA 2019 Solution View → 88

The mean of 5 observations is 4.4 and variance is 8.24 . If three of the five observations are 1,2 and 6, then what are the other two observations?

NDA 2019 Solution View → 89

Consider the following discrete frequency distribution: array lcccccccc x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 f & 3 & 15 & 45 & 57 & 50 & 36 & 25 & 9 array What is the value of median

NDA 2019 Solution View → 90

Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?

NDA 2019 Solution View → 91

If V is the variance and M is the mean of first 15 natural numbers, then what is V + M ^2 equal to?

NDA 2019 Solution View → 92

The mean of 100 observations is 50 and the standard deviation is 10 . If 5 is subtracted from each observation and then it is divided by 4 , then what will be the new mean and the

NDA 2019 Solution View → 93

Let the correlation coefficient between X and Y be 0.6 . Random variables Z and W are defined as Z=X+5 and W = Y 3 . What is the correlation coefficient between Z and W ?

NDA 2019 Solution View → 94

If all the natural numbers between 1 and 20 are multiplied by 3 , then what is the variance of the resulting series ?

NDA 2019 Solution View → 95

If the range of a set of observations on a variable X is known to be 25 and if Y=40+3 X , then what is the range of the set of corresponding observations on Y?

NDA 2019 Solution View → 96

Consider the following statements: 1. The algebraic sum of deviations of a set of values from their arithmetic mean is always zero. 2. Arithmetic mean Median Mode for a symmetric d

NDA 2019 Solution View → 97

Consider the following statements: 1. If 10 is added to each entry on a list then the average increase by 10 . 2. If 10 is added to each entry on a list, then the standard deviatio

NDA 2018 Solution View → 98

If the regression coefficient of Y on X is -6 , and the correlation coefficient between X and Y is - 1 2 , then the regression coefficient of X on Y would be

NDA 2018 Solution View → 99

The set of bivariate observation ( x ₁, y ₁ ), ( x ₂, y ₂ ), . . ( x _ n , y _ n ) are such that all the values are distinct and all the observations fall on a straight line with n

NDA 2018 Solution View → 100

In any discrete series (when all values are not same) if x represents mean deviation about mean and y represents standard deviation, then which one of the following is correct?

NDA 2018 Solution View → 101

An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry the following result: The average of monthly wages and variance of distribution

NDA 2018 Solution View → 102

The variance of 25 observations is 4 . If 2 is added to each observation, then the new variance of the resulting observations is

NDA 2018 Solution View → 103

In which one of the following cases would you except to get a negative correlation?

NDA 2018 Solution View → 104

The correlation coefficient computed from a set of 30 observations is 0.8 . Then the percentage of variation not explained by linear regression is

NDA 2018 Solution View → 105

If the correlation coefficient between x and y is 0.6 , covariance is 27 and variance of y is 25 , then what is the variance of x ?

NDA 2018 Solution View → 106

Let x be the mean of x₁, x₂, x₃, , x_n . If x_i=a+cy_i for some constants a and c , then what will be the mean of y ₁, y ₂, y ₃, ., y _ n ?

NDA 2018 Solution View → 107

Consider the following statements: 1. If the correlation coefficient r_ x y =0 , then the two lines of regression are parallel to each other. 2. If the correlation coefficient r _

NDA 2018 Solution View → 108

Consider the following statements: 1. Mean is independent of change in scale and change in origin. 2. Variance is independent of change in scale but not in origin. Which of the abo

NDA 2018 Solution View → 109

In a test in Mathematics, 20 % of the students obtained "first class". If the data are represented by a Pie-Chart, what is the central angle corresponding to "first class"?

NDA 2018 Solution View → 110

Consider the following statements: 1. The sum of deviations from mean is always zero. 2. The sum of absolute deviations is minimum when taken around median. Which of the above stat

NDA 2018 Solution View → 111

The standard deviation of the first N natural numbers can be obtained using which one of the following formulae?

NDA 2018 Solution View → 112

What is the median of the numbers 4.6,0,9.3,-4.8,7.6,2.3, 12.7,3.5, 8.2,6.1,3.9, 5.2?

NDA 2018 Solution View → 113

Which one of the following can be obtained from an ogive?

NDA 2018 Solution View → 114

The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the new set of values?

NDA 2018 Solution View → 115

Given that the arithmetic mean and standard deviation of a sample of 15 observations are 24 and 0 respectively. Then which one of the following is the arithmetic mean of the smalle

NDA 2017 Solution View → 116

Consider the following statements : 1. Variance is unaffected by change of origin and change of scale. 2. Coefficient of variance is independent of the unit of observations. Which

NDA 2017 Solution View → 117

The following table gives the monthly expenditure of two families: In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the fo

NDA 2017 Solution View → 118

The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is

NDA 2017 Solution View → 119

The variance of 20 observations is 5 . If each observation is multiplied by 3 , then what is the new variance of the resulting observations?

NDA 2017 Solution View → 120

The mean of a group of 100 observations was found to be 20 . Later it was found that four observations were incorrect, which were recorded as 21,21,18 and 20 . What is the mean if

NDA 2017 Solution View →
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