Statistics · NDA previous year questions

Directions: For the next 3 (three) questions to follow: The table below gives an incomplete frequency distribution with two missing frequencies $f_1$ and $f_2$. $$\begin{array}{ll}\text{Value of X}& \text{Frequency}\\ 0& f_1\\ 1& f_2\\ 2& 4\\ 3& 4\\ 4& 3\end{array}$$ The total frequency is 18 and the arithmetic mean of X is 2. What is the coefficient of variance?

1. A.$\frac{200}{3}$
2. B.$\frac{50\sqrt{5}}{9}$
3. C.$\frac{600}{\sqrt{5}}$
4. D.150

What is the sum of all natural numbers between 200 and 400 which are divisible by 7?

1. A.6729
2. B.8712
3. C.8729
4. D.9276

The mean and variance of a binomial distribution are 8 and 4 respectively. What is $P(X=1)$ equal to?

1. A.$\frac{1}{2^{12}}$
2. B.$\frac{1}{2^8}$
3. C.$\frac{1}{2^6}$
4. D.$\frac{1}{2^4}$

The geometric mean of three numbers was computed as 6. It was subsequently found that, in this computation, a number 8 was wrongly read as 12. What is the correct geometric mean?

1. A.4
2. B.$\sqrt[3]{5}$
3. C.$2\sqrt[3]{18}$
4. D.None of the above

A class consists of 3 sections A, B and C with 35, 35 and 30 students respectively. The arithmetic means of the marks secured by students of sections A and B, who appeared for a test of 100 marks are 74 and 70 respectively. The arithmetic mean of the marks secured by students of section C, who appeared for a test in the same subject which carried 75 marks is 51. What is the average percentage of marks secured by all the 100 students of the three sections ?

1. A.70.0
2. B.70.8
3. C.65.0
4. D.67.5

In a town 35·4% of the people are not literates, 27% have education up to primary school, 18·6% have education up to middle school. The people with education up to high school are twice the number of people with education up to Pre-University. Of the remaining, 660 are graduates. If the population of the town is 15,000, then what is the number of people with education up to high school ?

1. A.3120
2. B.1560
3. C.1460
4. D.None of the above

In a study on the relationship between investment $(X)$ and profit $(Y)$, the following two regression equations were obtained based on the data on $X$ and $Y$ : $$3X+Y-12=0$$ $$X+2Y-14=0.$$ What is the mean $\bar{X}$ ?

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

Following table gives the mean and variance of monthly demand for four products A, B, C and D in a supermarket : | Product | A | B | C | D | | --- | --- | --- | --- | --- | | Mean demand | 60 | 90 | 80 | 120 | | Variance | 12 | 25 | 36 | 16 | For which product the demand is consistent ?

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

What is the least value of the standard deviation of 5 integers, no two of which are equal ?

1. A.$\sqrt{5}$
2. B.2
3. C.$\sqrt{2}$
4. D.No such least value can be computed

MCQ (More than One Correct Answer) Correlation between two variables is said to be perfect if

1. A.one variable increases, the other also increases
2. B.one variable increases, the other decreases
3. C.one variable increases, the other also increases proportionally
4. D.one variable increases, the other decreases proportionally

Consider the following statements : 1. The data, which are collected from the units or individual respondents directly for the purpose of certain study or information are known as primary data. 2. The data obtained in a census study are primary data. 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

Given that $P(A)=1/3$, $P(B)=3/4$ and $P(A\cup B)=11/12$, then what is $P(B\mid A)$ ?

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

In a geometric progression with first term $a$ and common ratio $r$, what is the arithmetic mean of first five terms?

1. A.$a+2r$
2. B.$a{r}^2$
3. C.$a(r^5-1)/(r-1)$
4. D.$a(r^5-1)/[5(r-1)]$

If $2x=3+5i$, then what is the value of $2x^3+2x^2-7x+72$?

1. A.$4$
2. B.$-4$
3. C.$8$
4. D.$-8$

If $A=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$, then what is $A(\mathrm{Adj}A)$ equal to?

1. A.$\left[\begin{array}{cc}0& 10\\ 10& 0\end{array}\right]$
2. B.$\left[\begin{array}{cc}10& 0\\ 0& 10\end{array}\right]$
3. C.$\left[\begin{array}{cc}1& 10\\ 10& 1\end{array}\right]$
4. D.$\left[\begin{array}{cc}10& 1\\ 1& 10\end{array}\right]$

What is the inverse of $\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$?

1. A.$\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
2. B.$\left[\begin{array}{ccc}0& 0& 1\\ 0& 1& 0\\ 1& 0& 0\end{array}\right]$
3. C.$\left[\begin{array}{ccc}-1& 0& 1\\ 0& -1& 0\\ 0& 0& -1\end{array}\right]$
4. D.$\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$

The average sales and standard deviation of sales for four months for a company are as follows: Month 1: average sales 30, standard deviation 2; Month 2: 57, 3; Month 3: 82, 4; Month 4: 28, 2. During which month are the sales most consistent?

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

The harmonic mean of two numbers is 21.6. If one of the numbers is 27, then what is the other number?

1. A.16.2
2. B.17.3
3. C.18
4. D.20

The marks scored by two students $A$ and $B$ in six subjects are given below: $A:71,56,55,75,54,49$ $B:55,74,83,54,38,52$ Which one of the following statements is most appropriate?

1. A.The average scores of $A$ and $B$ are same but $A$ is consistent
2. B.The average scores of $A$ and $B$ are not same but $A$ is consistent
3. C.The average scores of $A$ and $B$ are same but $B$ is consistent
4. D.The average scores of $A$ and $B$ are not same but $B$ is consistent

In a factory, there are 30 men and 20 women employees. If the average salary of men is Rs 4,050 and the average salary of all the employees is Rs 3,550, then what is the average salary of women?

1. A.Rs 3,800
2. B.Rs 3,300
3. C.Rs 3,000
4. D.Rs 2,800

What is the standard deviation of numbers 7, 9, 11, 13, 15?

1. A.2.2
2. B.2.4
3. C.2.6
4. D.2.8

If the monthly expenditure pattern of a person who earns a monthly salary of Rs 15,000 is represented in a pie diagram, then the sector angle of an item on transport expenses measures $15^{\circ }$. What is his monthly expenditure on transport?

1. A.Rs 450
2. B.Rs 625
3. C.Rs 675
4. D.Cannot be computed from the given data

If ${\sum }_{i=1}^n(x_i-2)=110$ and ${\sum }_{i=1}^n(x_i-5)=20$, then what is the mean?

1. A.$11/2$
2. B.$2/11$
3. C.$17/3$
4. D.$17/9$