# Topic: Statistics (Test 1)

Topic: Statistics
Q.1
A batsman scores runs in 10 innings as 38,70,48,34,42,55,63,46,54 and 44 , then the mean score is
A. 494
B. 0.494
C. 4.94
D. 49.4
Explaination / Solution:

Mean (x) =

= 494/10

= 49.4

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Q.2
The mean of 5 observations is 4.4. If three observations are 1,2 and 6 and the difference of the other two is 5, then the other two observations are:
A. 5 and 9
B. 9 and 4
C. 4 and 8
D. 5 and 7
Explaination / Solution:

Let other two numbers be and

Mean (x) = 4.4 =

this gives ......(1)

Also,        ........(2)

Therefore from (1) and (2)

x = 9 and  y = 4

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Q.3
Which one of the following average is most affected of extreme observations ?
A. G.M.
B. Mode
C. Median
D. A. M.
Explaination / Solution:

As A/M is calculated as the sum of all the observations divided by number of observations, so it is affected by if there is any change in the outliers

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Q.4
S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is
A. 7
B. 8
C. 5
D. 6
Explaination / Solution:

so it depends only on number of observations not on individual observations.

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Q.5
If the coefficient of variation between x and y is 0.28, covariance between x and y is 7.6, and the variance of x is 9, then the S.D. of the y series is
A. 10.05
B. 9.8
C. 9.05
D. 10.1
Explaination / Solution:

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Q.6
If the mean of the squares of first n natural numbers be 11, then n is equal to
A. - 13/ 2
B. 13
C. 5
D. 11
Explaination / Solution:

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Q.7
If the two lines of regression are at right angles , then ρ(X,Y) is equal to
A. 1
B. -1
C. 0
D. 1 or - 1
Explaination / Solution:

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Q.8
If mean = ( 3 median – mode ) x , then the value of x is
A. 1/2
B. 2
C. 3/2
D. 1
Explaination / Solution:

We know that, 3median = mode + 2 mean

so, mean= (3 median - mode)/2      ........(1)

comparing equation(1) with the given equation

therefore, x=1/2

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Q.9
Which of the following is not a measure of dispersion ?
A. mean deviation
B. variance
C. range
D. mean
Explaination / Solution:

it is the measure of central tendency

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Q.10
If the two lines of regression are 2x + y =7 and x + 2y = 7, then ρ(X,Y) is equal to
A. -1/4
B. - 1/ 2
C. 1/ 4
D. 1/ 2