Statistics · NDA previous year questions

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.$Y=-8+0.2X$

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.$\frac{n}{2}$

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

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

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.$5:4$

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.$x_1+x_2<2(\sqrt{x_1{x}_2}+1)$

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

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

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

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.$\frac{3}{4}$

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.$320^{\circ }$

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

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

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

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.$\frac{1}{4}$

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

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

Consider the following statements: 1. The mean and median are equal in symmetric distribution. 2. The range is the difference between the maximum value and the minimum value in the data. 3. 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?

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

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?

1. A.Mean and median
2. B.Median and mode
3. C.Mode only
4. D.Mean and mode

For 10 observations on price (x) and supply (y), the following data was obtained: $\sum x=130$, $\sum y=220$, $\sum x^2=2288$, $\sum y^2=5506$ and $\sum xy=3467$. What is the line of regression of y on x?

1. A.$y=0.91x+8.74$
2. B.$y=1.02x+8.74$
3. C.$y=1.02x-7.02$
4. D.$y=0.91x-7.02$

In a study of two groups, the following results were obtained: | | Group A | Group B | |---|---|---| | Sample size | 20 | 25 | | Sample mean | 22 | 23 | | Sample standard deviation | 10 | 12 | Which of the following statements is correct?

1. A.Group A is less variable than Group B because Group A's standard deviation is smaller.
2. B.Group A is less variable than Group B because Group A's sample size is smaller.
3. C.Group A is less variable than Group B because Group A's sample mean is smaller.
4. D.Group A is less variable than Group B because Group A's coefficient of variation is smaller.

Consider the following statements in respect of class intervals of grouped frequency distribution: 1. Class intervals need not be mutually exclusive. 2. Class intervals should be exhaustive. 3. Class intervals need not be of equal width. 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

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 $x-y$?

1. A.$\frac{{\sigma }_x{\sigma }_y}{{\sigma }_x^2+{\sigma }_y^2}$
2. B.$\frac{{\sigma }_x+{\sigma }_y}{2{\sigma }_x{\sigma }_y}$
3. C.$\frac{{\sigma }_x^2-{\sigma }_y^2}{{\sigma }_x^2+{\sigma }_y^2}$
4. D.$\frac{{\sigma }_y-{\sigma }_x}{{\sigma }_x{\sigma }_y}$

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?

1. A.0.4
2. B.0.5
3. C.0.6
4. D.0.7

What is the mean deviation from the mean of the numbers 10, 9, 21, 16, 24 ?

1. A.5.2
2. B.5.0
3. C.4.5
4. D.4.0