Statistics · NDA previous year questions

Direction: Consider the following for the next two (02) items that follow. The marks obtained by 60 students in a certain subject out of 75 are given below: $$\begin{array}{cc}\text{Marks}& \text{Number of Students}\\ 15-20& 4\\ 20-25& 5\\ 25-30& 11\\ 30-35& 6\\ 35-40& 5\\ 40-45& 8\\ 45-50& 9\\ 50-55& 6\\ 55-60& 4\\ 60-65& 2\end{array}$$ What is the median?

1. A.35
2. B.38
3. C.39
4. D.40

Direction: Consider the following for the next two (02) items that follow. The marks obtained by 60 students in a certain subject out of 75 are given below: $$\begin{array}{cc}\text{Marks}& \text{Number of Students}\\ 15-20& 4\\ 20-25& 5\\ 25-30& 11\\ 30-35& 6\\ 35-40& 5\\ 40-45& 8\\ 45-50& 9\\ 50-55& 6\\ 55-60& 4\\ 60-65& 2\end{array}$$ What is the mode?

1. A.27.27
2. B.27.73
3. C.27.93
4. D.28.27

What is the mean of natural numbers in the interval [15, 64]?

1. A.36.8
2. B.38.3
3. C.39.5
4. D.40.3

For the set of numbers x, x, x + 2, x + 3, x + 10 where x is a natural number, which of the following is/are correct? 1. Mean > Mode 2. Median > Mean 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

The mean of 10 observations is 5.5. If each observation is multiplied by 4 and subtracted from 44, then what is the new mean?

1. A.20
2. B.22
3. C.34
4. D.44

If g is the geometric mean of 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, then which one of the following is correct?

1. A.8 < g < 16
2. B.16 < g < 32
3. C.32 < g < 64
4. D.g > 64

If the harmonic mean of 60 and x is 48, then what is the value of x?

1. A.32
2. B.36
3. C.40
4. D.44

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

1. A.5
2. B.5.5
3. C.10
4. D.10.5

1. A.22
2. B.33
3. C.44
4. D.55

The third term of a GP is 3. What is the product of its first five terms?

1. A.81
2. B.243
3. C.729
4. D.Cannot be determined due to insufficient data

If M is the mean of n observations $x_1-k$, $x_2-k$, $x_3-k$, $\dots$, $x_n-k$, where k is any real number, then what is the mean of $x_1$, $x_2$, $x_3$, $\dots$, $x_n$?

1. A.M
2. B.M + k
3. C.M - k
4. D.kM

What is the sum of deviations of the variate values 73, 85, 92, 105, 120 from their mean?

1. A.-2
2. B.-1
3. C.0
4. D.5

Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?

1. A.5m = 4n
2. B.2m = n
3. C.4m = 5n
4. D.m = 4n

If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?

1. A.2025
2. B.450
3. C.45
4. D.4.5

For which of the following sets of numbers do the mean, median and mode have the same value?

1. A.12, 12, 12, 12, 24
2. B.6, 18, 18, 18, 30
3. C.6, 6, 12, 30, 36
4. D.6, 6, 6, 12, 30

The mean of 12 observations is 75. If two observation are discarded, then the mean of the remaining observations is 65. What is the mean of the discarded observations?

1. A.250
2. B.125
3. C.120
4. D.Cannot be determined due to insufficient data

The geometric mean of a set of observations is computed as 10. The geometric mean obtained when each observations $x_i$ is replaced by $3x_i^4$ is

1. A.810
2. B.900
3. C.30000
4. D.81000

If the mode of the scores 10, 12, 13, 15, 15, 13, 12, 10, x is 15, then what is the value of x?

1. A.10
2. B.12
3. C.13
4. D.15

Consider the following measures of central tendency for a set of N numbers: 1. Arithmetic mean. 2. Geometric mean. Which of the above uses/use all the data?

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

The numbers of Science, Arts and Commerce graduates working in a company are 30, 70 and 50 respectively. If these figures are represented by a pie chart, then what is the angle corresponding to Science graduates?

1. A.36°
2. B.72°
3. C.120°
4. D.168°

For a histogram based on a frequency distribution with unequal class intervals, the frequency of a class should be proportional to:

1. A.the height of the rectangle.
2. B.the area of the rectangle.
3. C.the width of the rectangle.
4. D.the perimeter of the rectangle.

The co-efficient of correlation is independent of:

1. A.change of scale only.
2. B.change of origin only.
3. C.both change of scale and change of origin.
4. D.neither change of scale nor change of origin.

The following tables gives the frequency distribution of number of peas per pea pod of 198 pods: $$\begin{array}{lccccccc}\text{Number of peas}& 1& 2& 3& 4& 5& 6& 7\\ \text{Frequency}& 4& 33& 76& 50& 26& 8& 1\end{array}$$ What is the median of this distribution?

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

If ${\lim }_{x\to a}\frac{a^x-x^a}{x^x-a^a}=-1$, then what is the value of a?

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

The numbers 4 and 9 have frequencies $x$ and $(x-1)$ respectively. If their arithmetic mean is 6, then what is the value of $x$?

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