Statistics · Mathematics · NDA
MCQ (Single Correct Answer)
1
The regression coefficients of a bivariate distribution are $$-$$0.64 and $$-$$0.36. Then, the correlation coefficient of the distribution is
NDA 2015 Paper 2
2
The geometric mean of the observations x1, x2, x3, ......., xn is G1. The geometric mean of the observations y1, y2, y3, ......, yn is G2. The geometric mean of observations $${{{x_1}} \over {{y_1}}},{{{x_2}} \over {{y_2}}},{{{x_3}} \over {{y_3}}},....,{{{x_n}} \over {{y_n}}}$$ is
NDA 2015 Paper 2
3
The arithmetic mean of 1, 8, 27, 64, ...... upto n terms is given by
NDA 2015 Paper 2
4
Consider the following statements.
I. The mean and median are equal in symmetric distribution.
II. The range is the difference between the maximum value and the minimum value in the data.
III. The sum of the areas of the rectangles in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis.
Which of the above statements are correct?
I. The mean and median are equal in symmetric distribution.
II. The range is the difference between the maximum value and the minimum value in the data.
III. The sum of the areas of the rectangles in the histogram is equal to the total area bounded by the frequency polygon and the horizontal axis.
Which of the above statements are correct?
NDA 2016 Paper 2
5
The scores of 15 students in an examination were recorded as 10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change?
NDA 2016 Paper 2
6
For 10 observations on price (x) and supply (y), the following data was obtained.
$$\Sigma$$x = 130, $$\Sigma$$y = 220, $$\Sigma$$x2 = 2288, $$\Sigma$$y2 = 5506 and $$\Sigma$$xy = 3467.
What is the line of regression of y on x?
$$\Sigma$$x = 130, $$\Sigma$$y = 220, $$\Sigma$$x2 = 2288, $$\Sigma$$y2 = 5506 and $$\Sigma$$xy = 3467.
What is the line of regression of y on x?
NDA 2016 Paper 2
7
In a study of two groups, the following results were obtained.
Image
Which of the following statements is correct?
Image
Which of the following statements is correct?
NDA 2016 Paper 2
8
Consider the following statements in respect of class intervals of grouped frequency distribution.
I. Class-intervals need not be mutually exclusive.
II. Class-intervals should be exhaustive
III. Class-intervals need not be of equal width
Which of the above statements are correct?
I. Class-intervals need not be mutually exclusive.
II. Class-intervals should be exhaustive
III. Class-intervals need not be of equal width
Which of the above statements are correct?
NDA 2016 Paper 2
9
Two variates, x and y are uncorrelated and have standard deviations $$\sigma$$x and $$\sigma$$y respectively. What is the correlation coefficient between x + y and x $$-$$ y ?
NDA 2016 Paper 2
10
If the covariance between x and y is 30, variance of x is 25 and variance of y is 144, then what is the correlation coefficient?
NDA 2016 Paper 2
11
A random sample of 20 people is classified in the following table according to their ages.
What is the mean age of this group of people?
| Age | Frequency |
|---|---|
| 15-25 | 2 |
| 25-35 | 4 |
| 35-45 | 6 |
| 45-55 | 5 |
| 55-65 | 3 |
What is the mean age of this group of people?
NDA 2016 Paper 2
12
What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24 ?
NDA 2016 Paper 1
13
If the total number of observations is 20, $$\sum {x_i^{}} $$ = 1000 and $$\sum {x_i^2} $$ = 84000, then what is the variance of the distribution?
NDA 2016 Paper 1
14
The mean of the series x1, x2, ........, xn is $$\overline X $$. If x2 is replaced by $$\lambda$$, then what is the new mean?
NDA 2016 Paper 1
15
For the data 3, 5, 1, 6, 5, 9, 5, 2, 8, 6 the mean, median and mode are x, y and z, respectively. Which one of the following is correct?
NDA 2016 Paper 1
16
Consider the following statements in respect of a histogram.
1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the X-axis.
2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.
Which of the above statements is/are correct?
1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the X-axis.
2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.
Which of the above statements is/are correct?
NDA 2016 Paper 1
17
If m is the geometric mean of $${\left( {{y \over z}} \right)^{\log (yz)}}$$, $${\left( {{z \over x}} \right)^{\log (zx)}}$$ and $${\left( {{x \over y}} \right)^{\log (xy)}}$$, then what is the value of m?
NDA 2016 Paper 1
18
Consider the following statements :
1. Coefficient of variation depends on the unit of measurement of the variable.
2. Range is a measure of dispersion.
3. Mean deviation is least when measured about median.
Which of the above statements are correct?
1. Coefficient of variation depends on the unit of measurement of the variable.
2. Range is a measure of dispersion.
3. Mean deviation is least when measured about median.
Which of the above statements are correct?
NDA 2017 Paper 2
19
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 smallest five observations in the data?
NDA 2017 Paper 2
20
Which one of the following can be considered as appropriate pair of values of regression coefficient of y on x and regression coefficient of x on y ?
NDA 2017 Paper 2
21
It is given that $$\overline X = 10$$, $$\overline Y = 90$$, $${\sigma _X} = 3$$, $${\sigma _Y} = 12$$ and $${r_{XY}} = 0.8$$. The regression equation of X on Y is
NDA 2017 Paper 2
22
If a variable takes values 0, 1, 2, 3, ......., n with frequencies 1, C(n, 1), C(n, 2), C(n, 3), ......., C(n, n) respectively, then the arithmetic mean is
NDA 2017 Paper 2
23
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 of the statements given above is/are correct?
1. Variance is unaffected by change of origin and change of scale.
2. Coefficient of variance is independent of the unit of observations.
Which of the statements given above is/are correct?
NDA 2017 Paper 2
24
The coefficient of correlation when coefficients of regression are 0.2 and 1.8 is
NDA 2017 Paper 2
25
The variance of 20 observations is 5. If each observation is multiplied by 3, then what is new variance of the resulting observations?
NDA 2017 Paper 1
26
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 the incorrect observation are omitted?
NDA 2017 Paper 1
27
The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. What is the number of boys in the class?
NDA 2017 Paper 1
28
If two regression lines between height (x) and weight (y) are 4y $$-$$ 15x + 410 = 0 and 30x $$-$$ 2y $$-$$ 825 = 0, then what will be the correlation coefficient between height and weight?
NDA 2017 Paper 1
29
In an examination, 40% of candidates got second class. When the data are represented by a pie chart, wheat is the angle corresponding to second class?
NDA 2017 Paper 1
30
Consider the following statements :
Statement 1 : Range is not a good measure of dispersion.
Statement 2 : Range is highly affected by the existence of extreme values.
Which one of the following is correct in respect of the above statements?
Statement 1 : Range is not a good measure of dispersion.
Statement 2 : Range is highly affected by the existence of extreme values.
Which one of the following is correct in respect of the above statements?
NDA 2017 Paper 1
31
If the data are moderately non-symmetrical, then which one of the following empirical relationships is correct?
NDA 2017 Paper 1
32
Data can be represented in which of the following forms ?
1. Textual form
2. Tabular form
3. Graphical form
Select the correct answer using the code given below.
1. Textual form
2. Tabular form
3. Graphical form
Select the correct answer using the code given below.
NDA 2017 Paper 1
33
For given statistical data, the graphs for less than ogive and more than ogive are drawn. If the point at which the two curves intersect is P, then abscissa of point P gives the value of which one of the following measures of central tendency?
NDA 2017 Paper 1
34
If the regression coefficient of x on y and y on x are $$ - {1 \over 2}$$ and $$ - {1 \over 8}$$, respectively then what is the correlation coefficient between x and y?
NDA 2017 Paper 1
35
A sample of 5 observations has mean 32 and median 33. Later it is found that an observation was recorded incorrectly as 40 instead of 35. If we correct the data, then which one of the following is correct?
NDA 2017 Paper 1
36
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 Paper 2
37
The average age of a combined group of mean and women is 25 yr. If the average age of the group of men is 26 yr. and that of the group of women is 21 yr, then the percentage of men and women in the group is respectively
NDA 2018 Paper 2
38
Consider the following statements
1. If 10 is added to each entry on a lists, then the average increases by 10.
2. If 10 is added to each entry on a list, then the standard deviation increases by 10.
3. If each entry on a list is doubled then the average doubles.
Which of the above statements are correct?
1. If 10 is added to each entry on a lists, then the average increases by 10.
2. If 10 is added to each entry on a list, then the standard deviation increases by 10.
3. If each entry on a list is doubled then the average doubles.
Which of the above statements are correct?
NDA 2018 Paper 2
39
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 Paper 2
40
If the regression coefficient of Y on X is $$-$$6 and the correlation coefficient between X and Y is $$ - {1 \over 2}$$, then the regression coefficient of X on Y would be
NDA 2018 Paper 2
41
The set of bivariate observations (x1, y1), (x2, y2), ....... (xn, yn) are such that all the values are distinct and all the observations fall on a straight line with non-zero slope. Then, the possible values of the correlation coefficient between x and y are
NDA 2018 Paper 2
42
An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry gives the following result
Image
The average of monthly wage and variance of distribution of wages of all the workers in the firms A and B taken together are
Image
The average of monthly wage and variance of distribution of wages of all the workers in the firms A and B taken together are
NDA 2018 Paper 2
43
Which one of the following can be obtained from an ogive?
NDA 2018 Paper 2
44
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 Paper 2
45
In which one of the following cases would you expect to get negative correlation?
NDA 2018 Paper 2
46
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 Paper 1
47
Let $$\overline x $$ be the mean of x1, x2, x3, ....., xn. If xi = a + cyi for some constants a and c, then what will be the mean of y1, y2, y3, ....., yn ?
NDA 2018 Paper 1
48
Consider the following statements
I. If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other.
II. If the correlation coefficient rxy = 1, then the two lines of regression are perpendicular to each other.
Which of the above statements is/are correct?
I. If the correlation coefficient rxy = 0, then the two lines of regression are parallel to each other.
II. If the correlation coefficient rxy = 1, then the two lines of regression are perpendicular to each other.
Which of the above statements is/are correct?
NDA 2018 Paper 1
49
If 4x $$-$$ 5y + 33 = 0 and 20x $$-$$ 9y = 107 are two lines of regression, then what are the values of $$\overline x $$ and $$\overline y $$ respectively ?
NDA 2018 Paper 1
50
Consider the following statements
I. Mean is independent of change in scale and change in origin.
II. Variance is independent of change in scale but not in origin.
Which of the above statements is/are correct?
I. Mean is independent of change in scale and change in origin.
II. Variance is independent of change in scale but not in origin.
Which of the above statements is/are correct?
NDA 2018 Paper 1
51
Consider the following statements
I. The sum of deviations from mean is always zero.
II. The sum of absolute deviations is minimum when taken around median.
Which of the above statements is/are correct?
I. The sum of deviations from mean is always zero.
II. The sum of absolute deviations is minimum when taken around median.
Which of the above statements is/are correct?
NDA 2018 Paper 1
52
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 Paper 1
53
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 Paper 1
54
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 Paper 1
55
The standard deviation $$\sigma$$ of the first N natural numbers can be obtained using which one of the following formulae?
NDA 2018 Paper 1
56
If V is the variance and M is the numbers, then what is V + M2 equal to ?
NDA 2019 Paper 2
57
If the range of a set of observations on a variable X is known to be 25 and if Y = 40 + 3X, then what is the range of the set of corresponding observations on Y?
NDA 2019 Paper 2
58
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 Paper 2
59
Consider the following discrete frequency distribution.
Image
What is the value of median of the distribution ?
Image
What is the value of median of the distribution ?
NDA 2019 Paper 2
60
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 Paper 2
61
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 Paper 2
62
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 Paper 2
63
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 5th and 6th observations respectively?
NDA 2019 Paper 2
64
If two variables X and Y are independent, then what is the correlation coefficient between them?
NDA 2019 Paper 1
65
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 distribution.
Which of the above statements is/are correct?
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 distribution.
Which of the above statements is/are correct?
NDA 2019 Paper 1
66
Let the correlation coefficient between X and Y be 0.6. Random variables Z and W are defined as Z = X + 5 and W = $${Y \over 3}$$. What is the correlation coefficient between Z and W ?
NDA 2019 Paper 1
67
If all the natural numbers between 1 and 20 are multiplied by 3, then what is the variance on the resulting series?
NDA 2019 Paper 1
68
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 new standard deviation respectively?
NDA 2019 Paper 1
69
From data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as $y = a + bx$, then what is the value of $2a + 15b$?
NDA Mathematics 21 April 2024
70
If two random variables $X$ and $Y$ are connected by relation
$\frac{2 X-3 Y}{5 X+4 Y}=4$ and $X$ follows Binomial distribution with parameters $n=10$ and $p=\frac{1}{2}$, then what is the variance of $Y$ ?
NDA Mathematics 21 April 2024
71
An edible oil is sold at the rates 150, 200, 250, 300 rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family in every year during these years, what is the average price of oil in rupees (approximately) per litre?
NDA Mathematics 21 April 2024
72
$$
\text { What is } \sum_i^n x_i f_i \text { equal to? }
$$
NDA Mathematics 21 April 2024
73
What is the mean of the distribution?
NDA Mathematics 21 April 2024
74
What is the mean deviation of the largest five observations?
NDA Mathematics 21 April 2024
75
What is the variance of the largest five observations?
NDA Mathematics 21 April 2024
76
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 Mathematics 3 September 2023
77
If X̅ = 20 is the mean of 10 observations x1, x2, ... x10; then what is the value of $\displaystyle \sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right) ?$ ?
NDA Mathematics 3 September 2023
78
If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?
NDA Mathematics 3 September 2023
79
If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?
NDA Mathematics 3 September 2023
80
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 Mathematics 16 April 2023
81
The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. What is the value of 4p - q ?
NDA Mathematics 16 April 2023
82
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 what is (2m + M) equal to ?
NDA Mathematics 16 April 2023
83
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 Mathematics 16 April 2023
84
Consider the following frequency distribution :
| x | 1 | 2 | 3 | 5 |
| f | 4 | 6 | 9 | 7 |
What is the value of median of the distribution ?
NDA Mathematics 16 April 2023
85
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 4M - N ?
NDA Mathematics 16 April 2023
86
Let P, Q, R represent mean, median and mode. If for some distribution $5 P=4 Q=\frac{R}{2}$ then what is $\frac{P+Q}{2 P+0.7 R}$ equal to ?
NDA Mathematics 16 April 2023
87
Let P be the median, Q be the mean and R be the mode of observations x1, x2, x3, .....xn. Let $S=\sum\limits_{i=1}^n\left(2 x_i-a\right)^2$ S takes minimum value, when a is equal to
NDA Mathematics 16 April 2023
88
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 to celebrate the silver jubilee of their marriage. The coefficient of correlation at that point of time will be
NDA Mathematics 4 September 2022
89
Which one of the following subjects shows highest variability of marks ?
NDA Mathematics 4 September 2022
90
What is the coefficient of variation of marks in Mathematics ?
NDA Mathematics 4 September 2022
91
What is the median of the distribution ?
NDA Mathematics 4 September 2022
92
What is mean deviation about the median ?
NDA Mathematics 4 September 2022
93
What is the mean deviation about the mean ?
NDA Mathematics 4 September 2022
94
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 Mathematics 10 April 2022
95
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 Mathematics 10 April 2022
96
What is the coefficient of mean deviation of 21, 34, 23, 39, 26, 37, 40, 20, 33, 27 (taken from mean)?
NDA Mathematics 10 April 2022
97
What is the mean of the values?
NDA Mathematics 10 April 2022
98
What is the algebraic sum of the deviations of the same set of values measured from 99?
NDA Mathematics 10 April 2022
99
If the algebraic sum of the deviations of the same set of values measured from y is 180, then what is the value of y ?
NDA Mathematics 10 April 2022
100
What is the value of p ?
NDA Mathematics 10 April 2022
101
What is the value of q ?
NDA Mathematics 10 April 2022
102
If the frequency of each class is doubled, then what would be the mean?
NDA Mathematics 10 April 2022
103
If M is the mean of n observations x1 - k, x2 - k, x3 - k, _ _ _, xn - k, where k is any real number, then what is the mean of x1, x2, x3, _ _ _, xn?
NDA Mathematics 18 April 2021
104
What is the sum of deviations of the variate values 73, 85, 92, 105, 120 from their mean?
NDA Mathematics 18 April 2021
105
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 Mathematics 18 April 2021
106
For which of the following sets of numbers do the mean, median and mode have the same value?
NDA Mathematics 18 April 2021
107
The mean of 12 observations is 75. If two observation are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?
NDA Mathematics 18 April 2021
108
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 correcting the observation, the average is
NDA Mathematics 18 April 2021
109
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 Mathematics 18 April 2021
110
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 Mathematics 18 April 2021
111
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 corresponding to Science graduates?
NDA Mathematics 18 April 2021
112
For a histogram based on a frequency distribution with unequal class intervals, the frequency of a class should be proportional to:
NDA Mathematics 18 April 2021
113
The co-efficient of correlation is independent of:
NDA Mathematics 18 April 2021
114
The following tables gives the frequency distribution of number of peas per pea pod of 198 pods:
|
Number of peas |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
Frequency |
4 |
33 |
76 |
50 |
26 |
8 |
1 |
What is the median of this distribution?
NDA Mathematics 18 April 2021