Statistics · NDA previous year questions

What is the arithmetic mean of $8^2,9^2,10^2,\dots ,15^2$?

1. A.133.5
2. B.135.5
3. C.137.5
4. D.139.5

Direction: Consider the following for the items that follow: A triangle ABC is inscribed in the circle $x^2+y^2=100$. B and C have coordinates (6, 8) and (-8, 6) respectively. What are the coordinates of A?

1. A.(-6, 8)
2. B.(-6, -8)
3. C.$(5\sqrt{2},5\sqrt{2})$
4. D.Cannot be. determined due to insufficient data

Let $x-3y+4=0$ and $2x-7y+8=0$ be two lines of regression computed from some bivariate data. If $b_{yx}$ and $b_{xy}$ are regression coefficients of lines of regression of y on x and x on y respectively, then what is the value of $b_{xy}+7b_{yx}$?

1. A.-2
2. B.1
3. C.2
4. D.5

The mean of n observations 1, 4, 9, 16 ...., $n^2$ is 130. What is the value of n?

1. A.18
2. B.19
3. C.20
4. D.21

What is the mean deviation of the first 10 natural numbers?

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

Let ${\sum }_{i=1}^9{x}_i^2=855$ If M is the mean and $\sigma$ is the standard deviation of $x_1,x_2,x_3.....x_9$ then what is the value of $M^2+{\sigma }^2$?

1. A.100
2. B.95
3. C.90
4. D.85

The mean of the series $x_1,x_2\dots x_n$ is $\bar{x}$ If $x_n$ is replaced by k, then what is the new mean?

1. A.$\bar{x}-x_n+k$
2. B.$\frac{n\bar{x}-\bar{x}+k}{n}$
3. C.$\frac{\bar{x}-x_n-k}{n}$
4. D.$\frac{n\bar{x}-x_n+k}{n}$

In a binomial distribution, if the mean is 6 and the standard deviation is √2, then what are the values of the parameters n and p respectively?

1. A.18 and 1/3
2. B.9 and 1/3
3. C.18 and 2/3
4. D.9 and 2/3

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 $2a+15b$?

1. A.6
2. B.11
3. C.17
4. D.21

Let $x+2y+1=0$ and $2x+3y+4=0$ are two lines of regression computed from some bivariate data. If $\theta$ is the acute angle between them, then what is the value of $488\tan 3\theta$ ?

1. A.191
2. B.161
3. C.131
4. D.121

Consider the following for the next two (02) items that follow: $$\begin{array}{cccccc}{x}_i& 1& 2& 3& \dots & n\\ f_i& 1& 2^{-1}& 2^{-2}& \dots & 2^{-(n-1)}\end{array}$$ What is the mean of the distribution?

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

Consider the following for the next two (02) items that follow: The marks obtained by 10 students in a Statistics test are 24, 47, 18, 32, 19, 15, 21, 35, 50 and 41. What is the mean deviation of the largest five observations?

1. A.4.8
2. B.5.5
3. C.6
4. D.7.5

What is the variance of the largest five observations?

1. A.14.6
2. B.21.8
3. C.25.2
4. D.46.8

If $\bar{X}=20$ is the mean of 10 observations $x_1,x_2,\dots x_{10}$; then what is the value of ${\sum }_{i=1}^{10}\left(\frac{3x_i-4}{5}\right)$?

1. A.0
2. B.12
3. C.112
4. D.1012

If the mean and the sum of squares of 10 observations are 40 and 16160 respectively, then what is the standard deviation?

1. A.16
2. B.6
3. C.5
4. D.4

What is the mean of the numbers 1, 2, 3, ... 10 with frequencies ${}^9{C}_0,{}^9{C}_1,{}^9{C}_2\dots ,{}^9{C}_9$, respectively?

1. A.$1.1\times 2^8$
2. B.$1.2\times 7^4$
3. C.5.5
4. D.0.55

If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?

1. A.-r
2. B.r
3. C.√3 r
4. D.-√3r

If H is the Harmonic Mean of three numbers ${}^{10}{C}_4$, ${}^{10}{C}_5$, and ${}^{10}{C}_6$, then what is the value of $\frac{270}{H}$ ?

1. A.1
2. B.$\frac{14}{17}$
3. C.$\frac{17}{14}$
4. D.$\frac{1}{31}$

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 ?

1. A.8 and 15
2. B.9 and 14
3. C.10 and 13
4. D.11 and 12

If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?

1. A.-13
2. B.-5
3. C.5
4. D.7

A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?

1. A.x - 4y + 5 = 0
2. B.3x + 2y - 1 = 0
3. C.x + 4y + 1 = 0
4. D.5x - 4y + 1 = 0

Consider the following frequency distribution : $$\begin{array}{ccccc}x& 1& 2& 3& 5\\ f& 4& 6& 9& 7\end{array}$$ What is the value of median of the distribution ?

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

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 ?

1. A.7
2. B.4
3. C.1
4. D.0

Let P, Q, R represent mean, median and mode. If for some distribution $5P=4Q=\frac{R}{2}$ then what is $\frac{P+Q}{2P+0.7R}$ equal to ?

1. A.$\frac{1}{12}$
2. B.$\frac{1}{7}$
3. C.$\frac{2}{9}$
4. D.$\frac{1}{4}$

If G is the geometric mean of numbers $1,2,2^2,2^3,\dots ,2^{n-1}$, then what is the value of $1+2{\log }_{2}G$ ?

1. A.1
2. B.4
3. C.n - 1
4. D.n