Statistics · NDA previous year questions

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?

1. A.1500
2. B.1600
3. C.1700
4. D.1800

The mean of the series $x_1,x_2,\dots ,x_n$ is $\overline{X}$. If $x_2$ is replaced by $\lambda$, then what is the new mean?

1. A.$\overline{X}-x_2+\lambda$
2. B.$\frac{\overline{X}-x_2-\lambda }{n}$
3. C.$\frac{\overline{X}-x_2+\lambda }{n}$
4. D.$\frac{n\overline{X}-x_2+\lambda }{n}$

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?

1. A.$x=y\ne z$
2. B.$x\ne y=z$
3. C.$x\ne y\ne z$
4. D.$x=y=z$

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

If $m$ is the geometric mean of ${\left(\frac{y}{z}\right)}^{\log (yz)}$, ${\left(\frac{z}{x}\right)}^{\log (zx)}$ and ${\left(\frac{x}{y}\right)}^{\log (xy)}$ then what is the value of $m$?

1. A.1
2. B.3
3. C.6
4. D.9

The regression coefficients of a bivariate distribution are $-0.64$ and $-0.36$. Then the correlation coefficient of the distribution is

1. A.0.48
2. B.$-0.48$
3. C.0.50
4. D.$-0.50$

The geometric mean of the observations $x_1,x_2,x_3,\dots ,x_n$ is $G_1$. The geometric mean of the observations $y_1,y_2,y_3,\dots ,y_n$ is $G_2$. The geometric mean of observations $\frac{x_1}{y_1},\frac{x_2}{y_2},\frac{x_3}{y_3},\dots ,\frac{x_n}{y_n}$ is

1. A.$G_1{G}_2$
2. B.$\ln (G_1{G}_2)$
3. C.$\frac{G_1}{G_2}$
4. D.$\ln \left(\frac{G_1}{G_2}\right)$

The arithmetic mean of $1,8,27,64,\dots$ up to $n$ terms is given by

1. A.$\frac{n(n+1)}{2}$
2. B.$\frac{n(n+1{)}^2}{2}$
3. C.$\frac{n(n+1{)}^2}{4}$
4. D.$\frac{n^2(n+1{)}^2}{4}$

The mean and the variance of 10 observations are given to be 4 and 2 respectively. If every observation is multiplied by 2, the mean and the variance of the new series will be respectively

1. A.8 and 20
2. B.8 and 4
3. C.8 and 8
4. D.80 and 40

Which one of the following measures of central tendency is used in construction of index numbers?

1. A.Harmonic mean
2. B.Geometric mean
3. C.Median
4. D.Mode

The correlation coefficient between two variables $X$ and $Y$ is found to be 0.6. All the observations on $X$ and $Y$ are transformed using the transformations $U=2-3X$ and $V=4Y+1$. The correlation coefficient between the transformed variables $U$ and $V$ will be

1. A.-0.5
2. B.+0.5
3. C.-0.6
4. D.+0.6

Which of the following statements is/are correct in respect of regression coefficients? 1. It measures the degree of linear relationship between two variables. 2. It gives the value by which one variable changes for a unit change in the other variable. 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

A set of annual numerical data, comparable over the years, is given for the last 12 years. Consider the following statements : 1. The data is best represented by a broken line graph, each corner (turning point) representing the data of one year. 2. Such a graph depicts the chronological change and also enables one to make a short-term forecast. 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

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is

1. A.28
2. B.30
3. C.35
4. D.38

The ‘less than’ ogive curve and the ‘more than’ ogive curve intersect at

1. A.median
2. B.mode
3. C.arithmetic mean
4. D.None of the above

For the next three (03) items that follow: Let $f(x)=a{x}^2+bx+c$ such that $f(1)=f(-1)$ and a, b, c are in Arithmetic Progression. What is the value of b?

1. A.-1
2. B.0
3. C.1
4. D.Cannot be determined due to insufficient data

Consider the following statements in respect of histogram: 1. The histogram is a suitable representation of a frequency distribution of a continuous variable. 2. The area included under the whole histogram is the total frequency. 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

The regression lines will be perpendicular to each other if the coefficient of correlation r is equal to

1. A.1 only
2. B.1 or -1
3. C.-1 only
4. D.0

If $\bar{x}$ and $\bar{y}$ are the means of two distributions such that $\bar{x}<\bar{y}$ and $\bar{z}$ is the mean of the combined distribution, then which one of the following statements is correct?

1. A.$\bar{x}<\bar{y}<\bar{z}$
2. B.$\bar{x}>\bar{y}>\bar{z}$
3. C.$\bar{z}=\frac{\bar{x}+\bar{y}}{2}$
4. D.$\bar{x}<\bar{z}<\bar{y}$

What is the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17?

1. A.2.5
2. B.3
3. C.3.5
4. D.4

The variance of 20 observations is 5. If each observation is multiplied by 2, then what is the new variance of the resulting observations?

1. A.5
2. B.10
3. C.20
4. D.40

For two variables $x$ and $y$, the two regression coefficients are $b_{yx}=-3/2$ and $b_{xy}=-1/6$. The correlation coefficient between $x$ and $y$ is:

1. A.$-1/4$
2. B.1/4
3. C.$-1/2$
4. D.1/2

The variance of numbers $x_1,x_2,x_3,\dots \dots x_n$ is $V$. Consider the following statements: 1. If every $x_i$ is increased by 2, the variance of the new set of numbers is $V$. 2. If the numbers $x_i$ is squared, the variance of the new set is $V^2$. Which of the following statements is/are correct?

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

What is the mean of the squares of the first 20 natural numbers?

1. A.151.5
2. B.143.5
3. C.65
4. D.72

$p,q,r,s,t$ are five numbers such that the average of $p,q$ and $r$ is 5 and that of $s$ and $t$ is 10. What is the average of all the five numbers?

1. A.7.75
2. B.7.5
3. C.7
4. D.5