Statistics · NDA previous year questions

2017 20 questions

1. Q892017 · 10 Sept 2017

   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. A.1 and 2 only
   2. B.2 and 3 only
   3. C.1 and 3 only
   4. D.1, 2 and 3
   Show answer

   Answer: B

2. Q902017 · 10 Sept 2017

   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?

   1. A.0
   2. B.8
   3. C.16
   4. D.24
   Show answer

   Answer: D

3. Q912017 · 10 Sept 2017

   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 $y$?

   1. A.$(1,1)$
   2. B.$(-1,1)$
   3. C.$\left(-\frac{1}{2},2\right)$
   4. D.$\left(\frac{1}{3},\frac{10}{3}\right)$
   Show answer

   Answer: A

4. Q922017 · 10 Sept 2017

   It is given that $\bar{X}=10$, $\bar{Y}=90$, ${\sigma }_X=3$, ${\sigma }_Y=12$ and $r_{XY}=0.8$. The regression equation of $X$ on $Y$ is

   1. A.$Y=3.2X+58$
   2. B.$X=3.2Y+58$
   3. C.$X=-8+0.2Y$
   4. D.$Y=-8+0.2X$
   Show answer

   Answer: C

5. Q932017 · 10 Sept 2017

   If a variable takes values $0,1,2,3,\dots ,n$ with frequencies $1,C(n,1),C(n,2),C(n,3),\dots ,C(n,n)$ respectively, then the arithmetic mean is

   1. A.$2n$
   2. B.$n+1$
   3. C.$n$
   4. D.$\frac{n}{2}$
   Show answer

   Answer: D

6. Q942017 · 10 Sept 2017

   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. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: B

7. Q952017 · 10 Sept 2017

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

   1. A.0.36
   2. B.0.2
   3. C.0.6
   4. D.0.9
   Show answer

   Answer: C

8. Q1192017 · 10 Sept 2017

   The following table gives the monthly expenditure of two families: $$\begin{array}{lll}& \text{Expenditure (in ₹)}& \\ \text{Items}& \text{Family A}& \text{Family B}\\ \text{Food}& \text{3,500}& \text{2,700}\\ \text{Clothing}& \text{500}& \text{800}\\ \text{Rent}& \text{1,500}& \text{1,000}\\ \text{Education}& \text{2,000}& \text{1,800}\\ \text{Miscellaneous}& \text{2,500}& \text{1,800}\end{array}$$ In constructing a pie diagram to the above data, the radii of the circles are to be chosen by which one of the following ratios?

   1. A.$1:1$
   2. B.$10:9$
   3. C.$100:91$
   4. D.$5:4$
   Show answer

   Answer: B

9. Q1202017 · 10 Sept 2017

   If $x_1$ and $x_2$ are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

   1. A.$x_1+x_2>2\sqrt{x_1{x}_2}$
   2. B.$\sqrt{x_1}+\sqrt{x_2}>\sqrt{2}$
   3. C.$|\sqrt{x_1}-\sqrt{x_2}|>\sqrt{2}$
   4. D.$x_1+x_2<2(\sqrt{x_1{x}_2}+1)$
   Show answer

   Answer: C

10. Q972017 · 23 Apr 2017

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

    1. A.5
    2. B.10
    3. C.15
    4. D.45
    Show answer

    Answer: D

11. Q982017 · 23 Apr 2017

    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 observations are omitted?

    1. A.18
    2. B.20
    3. C.21
    4. D.22
    Show answer

    Answer: B

12. Q992017 · 23 Apr 2017

    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?

    1. A.50
    2. B.55
    3. C.60
    4. D.100
    Show answer

    Answer: A

13. Q1002017 · 23 Apr 2017

    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?

    1. A.$\frac{1}{3}$
    2. B.$\frac{1}{2}$
    3. C.$\frac{2}{3}$
    4. D.$\frac{3}{4}$
    Show answer

    Answer: B

14. Q1012017 · 23 Apr 2017

    In an examination, 40% of candidates got second class. When the data are represented by a pie chart, what is the angle corresponding to second class?

    1. A.$40^{\circ }$
    2. B.$90^{\circ }$
    3. C.$144^{\circ }$
    4. D.$320^{\circ }$
    Show answer

    Answer: C

15. Q1032017 · 23 Apr 2017

    If the data are moderately non-symmetrical, then which one of the following empirical relationships is correct?

    1. A.$2\times$ Standard deviation $=5\times$ Mean deviation
    2. B.$5\times$ Standard deviation $=2\times$ Mean deviation
    3. C.$4\times$ Standard deviation $=5\times$ Mean deviation
    4. D.$5\times$ Standard deviation $=4\times$ Mean deviation
    Show answer

    Answer: C

16. Q1042017 · 23 Apr 2017

    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. A.1 and 2 only
    2. B.2 and 3 only
    3. C.1 and 3 only
    4. D.1, 2 and 3
    Show answer

    Answer: D

17. Q1052017 · 23 Apr 2017

    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?

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

18. Q1062017 · 23 Apr 2017

    If the regression coefficient of $x$ on $y$ and $y$ on $x$ are $-\frac{1}{2}$ and $-\frac{1}{8}$ respectively, then what is the correlation coefficient between $x$ and $y$?

    1. A.$-\frac{1}{4}$
    2. B.$-\frac{1}{16}$
    3. C.$\frac{1}{16}$
    4. D.$\frac{1}{4}$
    Show answer

    Answer: A

19. Q1072017 · 23 Apr 2017

    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?

    1. A.The mean and median remain the same
    2. B.The median remains the same but the mean will decrease
    3. C.The mean and median both will decrease
    4. D.The mean remains the same but median will decrease
    Show answer

    Answer: B

20. Q1152017 · 23 Apr 2017

    The mean and standard deviation of a binomial distribution are 12 and 2 respectively. What is the number of trials?

    1. A.2
    2. B.12
    3. C.18
    4. D.24
    Show answer

    Answer: C