Statistics · NDA previous year questions

2018 23 questions

1. Q932018 · 9 Sept 2018

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

   1. A.80%
   2. B.20%
   3. C.64%
   4. D.36%
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   Answer: D

2. Q942018 · 9 Sept 2018

   The average age of a combined group of men and women is 25 years. If the average age of the group of men is 26 years and that of the group of women is 21 years, then the percentage of men and women in the group is respectively

   1. A.20, 80
   2. B.40, 60
   3. C.60, 40
   4. D.80, 20
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   Answer: D

3. Q952018 · 9 Sept 2018

   Consider the following statements : 1. If 10 is added to each entry on a list, 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. A.1, 2 and 3
   2. B.1 and 2 only
   3. C.1 and 3 only
   4. D.2 and 3 only
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   Answer: C

4. Q962018 · 9 Sept 2018

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

   1. A.2
   2. B.4
   3. C.6
   4. D.8
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   Answer: B

5. Q972018 · 9 Sept 2018

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

   1. A.$\frac{1}{24}$
   2. B.$-\frac{1}{24}$
   3. C.$-\frac{1}{6}$
   4. D.$\frac{1}{6}$
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   Answer: B

6. Q982018 · 9 Sept 2018

   The set of bivariate observations $(x_1,y_1),(x_2,y_2),\dots ,(x_n,y_n)$ 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

   1. A.0 and 1 only
   2. B.0 and $-1$ only
   3. C.0, 1 and $-1$
   4. D.$-1$ and 1 only
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   Answer: D

7. Q992018 · 9 Sept 2018

   An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry gives the following result: $$\begin{array}{lll}& \text{Firm A}& \text{Firm B}\\ \text{Number of workers}& 500& 600\\ \text{Average monthly wage}& \text{₹ 1860}& \text{₹ 1750}\\ \text{Variance of distribution of wages}& 81& 100\end{array}$$ The average of monthly wage and variance of distribution of wages of all the workers in the firms A and B taken together are

   1. A.₹ 1860, 100
   2. B.₹ 1750, 100
   3. C.₹ 1800, 81
   4. D.None of the above
   Show answer

   Answer: D

8. Q1002018 · 9 Sept 2018

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

   1. A.Mean
   2. B.Median
   3. C.Geometric mean
   4. D.Mode
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   Answer: B

9. Q1012018 · 9 Sept 2018

   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?

   1. A.$y\ge x$
   2. B.$y\le x$
   3. C.$x=y$
   4. D.$x<y$
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   Answer: A

10. Q1022018 · 9 Sept 2018

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

    1. A.The ages of husbands and wives
    2. B.Shoe size and intelligence
    3. C.Insurance companies' profits and the number of claims they have to pay
    4. D.Amount of rainfall and yield of crop
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    Answer: C

11. Q1192018 · 9 Sept 2018

    If $\sin \beta$ is the harmonic mean of $\sin \alpha$ and $\cos \alpha$, and $\sin \theta$ is the arithmetic mean of $\sin \alpha$ and $\cos \alpha$, then which of the following is/are correct? 1. $\sqrt{2}\sin \left(\alpha +\frac{\pi }{4}\right)\sin \beta =\sin 2\alpha$ 2. $\sqrt{2}\sin \theta =\cos \left(\alpha -\frac{\pi }{4}\right)$ Select the correct answer using the code given below:

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
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    Answer: C

12. Q1202018 · 9 Sept 2018

    If $x_i>0,y_i>0(i=1,2,3,\dots n)$ are the values of two variables X and Y with geometric means P and Q respectively, then the geometric mean of $\frac{X}{Y}$ is

    1. A.$\frac{P}{Q}$
    2. B.antilog $\left(\frac{P}{Q}\right)$
    3. C.$n(\log P-\log Q)$
    4. D.$n(\log P+\log Q)$
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    Answer: A

13. Q142018 · 22 Apr 2018

    The third term of a GP is 3. What is the product of the first five terms ?

    1. A.216
    2. B.226
    3. C.243
    4. D.Cannot be determined due to insufficient data
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    Answer: C

14. Q932018 · 22 Apr 2018

    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?

    1. A.9/5
    2. B.81/25
    3. C.9
    4. D.81
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    Answer: D

15. Q942018 · 22 Apr 2018

    Let $\bar{x}$ be the mean of $x_1,x_2,x_3,\dots ,x_n$. If $x_i=a+c{y}_i$ for some constants a and c, then what will be the mean of $y_1,y_2,y_3,\dots ,y_n$?

    1. A.$a+c\bar{x}$
    2. B.$a-\frac{1}{c}\bar{x}$
    3. C.$\frac{1}{c}\bar{x}-a$
    4. D.$\frac{\bar{x}-a}{c}$
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    Answer: D

16. Q952018 · 22 Apr 2018

    Consider the following statements: 1. If the correlation coefficient $r_{xy}=0$, then the two lines of regression are parallel to each other. 2. If the correlation coefficient $r_{xy}=+1$, then the two lines of regression are perpendicular to each other. Which of the above statements is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
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    Answer: D

17. Q962018 · 22 Apr 2018

    If $4x-5y+33=0$ and $20x-9y=107$ are two lines of regression, then what are the values of $\bar{x}$ and $\bar{y}$ respectively?

    1. A.12 and 18
    2. B.18 and 12
    3. C.13 and 17
    4. D.17 and 13
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    Answer: C

18. Q972018 · 22 Apr 2018

    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 above statements is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
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    Answer: D

19. Q982018 · 22 Apr 2018

    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 statements is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
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    Answer: C

20. Q992018 · 22 Apr 2018

    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?

    1. A.3.8
    2. B.4.9
    3. C.5.7
    4. D.6.0
    Show answer

    Answer: B

21. Q1002018 · 22 Apr 2018

    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”?

    1. A.$20^{\circ }$
    2. B.$36^{\circ }$
    3. C.$72^{\circ }$
    4. D.$144^{\circ }$
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    Answer: C

22. Q1012018 · 22 Apr 2018

    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?

    1. A.10
    2. B.20
    3. C.40
    4. D.70
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    Answer: B

23. Q1022018 · 22 Apr 2018

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

    1. A.$\sigma =\frac{N^2-1}{12}$
    2. B.$\sigma =\sqrt{\frac{N^2-1}{12}}$
    3. C.$\sigma =\sqrt{\frac{N-1}{12}}$
    4. D.$\sigma =\sqrt{\frac{N^2-1}{6N}}$
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    Answer: B