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This contains 20 Multiple Choice Questions for GATE Test: Probability & Statistics (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If the arithmetic mean of two numbers is 10 and their geometric mean is 8, the numbers are

Solution:

Let the numbers be a and b Then

Solving a + b = 20 and a - b = 12 we get a = 16 and b = 4.

QUESTION: 2

The median of

0, 2, 2, 2, -3, 5, -1, 5, 5, -3, 6, 6, 5, 6 is

Solution:

Observations in ascending order are -3, -3, -1, 0, 2, 2, 2, 5, 5, 5, 5 6, 6, 6

Number of observations is 14, which is even.

QUESTION: 3

Consider the following table

The median of the above frequency distribution is

Solution:

The given Table may be presented as

QUESTION: 4

The mode of the following frequency distribution, is

Solution:

Maximum frequency is 23. So, modal class is 12–15.

QUESTION: 5

The mean-deviation of the data 3, 5, 6, 7, 8, 10, 11, 14 is

Solution:

QUESTION: 6

The mean deviation of the following distribution is

Solution:

QUESTION: 7

The standard deviation for the data 7, 9, 11, 13, 15 is

Solution:

QUESTION: 8

The standard deviation of 6, 8, 10, 12, 14 is

Solution:

QUESTION: 9

The probability that an event A occurs in one trial of an experiment is 0.4. Three independent trials of experiment are performed. The probability that A occurs at least once is

Solution:

Here p = 0.4, q = 0.6 and n = 3.

QUESTION: 10

Eight coins are tossed simultaneously. The probability of getting at least 6 heads is

Solution:

p = 1/2, q = 1/2, n = 8. Required probability = P (6 heads or 7 heads or 8 heads)

QUESTION: 11

The ranks obtained by 10 students in Mathematics and Physics in a class test are as follows

The coefficient of correlation between their ranks is

Solution:

D_{i} = -2, -8, -2, 3, 3, -3, 3, 0, 2, 4.

QUESTION: 12

If ∑x_{i} = 24, ∑y_{i} = 44, ∑x_{i}y_{i} = 306, ∑x_{i}^{2} =164 ,∑y_{i}^{2} = 574 and n = 4 then the regression coefficient b_{xy } is equal to

Solution:

QUESTION: 13

If ∑x_{i} = 30, ∑y_{i} = 42, ∑x_{i}y_{i} = 199 , ∑x_{i}^{2} =184 ,∑y_{i}^{2} = 318 and n = 6 then the regression coefficient b_{xy } is equal to

Solution:

QUESTION: 14

Let r be the correlation coefficient between x and y and b_{xy} ,b_{yx} be the regression coefficients of y on x and x on y respectively then

Solution:

QUESTION: 15

Which one of the following is a true statement

Solution:

QUESTION: 16

If b_{yx }= 1.6 and b_{xy} = 0.4 and θ is the angle between two regression lines, then tan θ is equal to

Solution:

QUESTION: 17

The equations of the two lines of regression are : 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0. The correlation coefficient between x and y is

Solution:

QUESTION: 18

If cov(X, Y) = 10, var (X) = 6.25 and var(Y) = 31.36, then ρ(X,Y) is

Solution:

QUESTION: 19

If ∑x = ∑y = 15, ∑x^{2} = ∑y^{2} = 49, ∑xy = 44 and n = 5, then b_{xy} = ?

Solution:

QUESTION: 20

If ∑x = 125, ∑y = 100 , ∑x^{2} = 1650, ∑y^{2} = 1500 , ∑xy = 50 and n = 25, then the line of regression of x on y is

Solution:

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