Test: Statistics- 1 - JEE MCQ

# Test: Statistics- 1 - JEE MCQ

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## 25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Statistics- 1

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Test: Statistics- 1 - Question 1

### A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44, then the mean deviation is

Detailed Solution for Test: Statistics- 1 - Question 1

Arranging the given data in ascending order,
we have 34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here, Median M = (46+48)/2
=47
(∵ n = 10, median is the mean of 5th and 6th items)
∴ Mean deviation = ∑|xi−M|/n
=∑|xi−47|/10
= (13+9+5+3+1+1+7+8+16+23)/10
=8.6

Test: Statistics- 1 - Question 2

### The S.D. of the observations 22,26,28,20,24,30 is

Detailed Solution for Test: Statistics- 1 - Question 2

μ = (22 + 26 + 28 + 20 + 24 + 30)/6
= 150/6
= 25
x(i) = (xi - μ)2
x(22) = (22-25)2 = 9
x(26) = (26-25)2 = 1
x(28) = (28-25)2 = 9
x(20) = (20-25)2 = 25
x(24) = (24-25)2 = 1
x(30) = (30-25)2 = 25

(xi - μ)2  = 70
Standard deviation : [(xi - μ)2]/N
= (70/6)½
= 3.42

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Test: Statistics- 1 - Question 3

### If the angle between two lines of regression is 900, then it represents

Test: Statistics- 1 - Question 4

The two lines of regression are 2x - 7y + 6 = 0 and 7x – 2y +1 = 0. What is correlation coefficient between x and y ?

Detailed Solution for Test: Statistics- 1 - Question 4

ρ = (b(xy) * b(yx))
But sign of ρρ is same as sign of b(xy), b(yx)
Therefore, ρ = 2/7

Test: Statistics- 1 - Question 5

The two lines of regression are x + 4y = 3 and 3x +y = 15. value of x for y = 3 is

Detailed Solution for Test: Statistics- 1 - Question 5

Given lines are x+4y=3   (i)
& 3x+y=15        (ii)
We first check which of the line (i) & (ii) is line of regression y
on x and x on y. Let line x+4y=3 be the line of regression x on y, then
other be the line of regression y on x.
∴ From (i) i.e. line of regression x on y we have x=−4y+3
∴ b(xy)=regression coefficient x on y=−4 and 3x+y=15
∴ y=−3x+15
∴ b(yx)=regression coefficient y on x=-3
Now count r2=b(yx)b(xy)=(−4)(−3)=12
⇒ ∣r∣=2(3)1/2
​which is not possible as 0≤r2≤1. So our assumption is wrong
and line x+4y=3 is line of regression y on x & 3x+y=15 is line of
regression x on y.
∴ 3x+y=15
⇒ x=(15−y)/3
⇒ x=(15−3)/3   (By putting y=3)
​= 4

Test: Statistics- 1 - Question 6

The mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1,2 and 6, the other two observations are

Detailed Solution for Test: Statistics- 1 - Question 6

Let the other nos. be a and b
then (x+y+1+2+6)/5 = 4.4
x + y = 13 ---------------------(1)
Variance = 8.24

41.2 = 19.88 + (x2 + 19.36 – 8.8x) + (y2 + 19.36 – 8.8y)
21.32 = x2 + y2 + 38.72 – 8.8(x + y)
x2 + y2 + 38.72 – 8.8(13) – 21.32 = 0
(using equation (1))
x2 + y2 – 97 = 0 …(2)
Squaring equation (1) both the sides,
we get (x + y)2 = (13)^2
x2 + y2 + 2xy = 169
97 + 2xy = 169
(using equation (2))
xy = 36 or x = 36/y (1)
⇒ 36/y + y = 13
y2 + 36 = 13y
y2 – 13y + 36 = 0
(y – 4)(y – 9) = 0
Either (y – 4) = 0 or (y – 9) = 0
⇒ y = 4 or y = 9
For y = 4 x = 36/y
= 36/4 = 12
For y = 9
x = 36/9
x = 4
Thus, remaining two observations are 4 and 9.

Test: Statistics- 1 - Question 7

If x and y are related as y – 4x = 3, then the nature of correlation between x and y is

Detailed Solution for Test: Statistics- 1 - Question 7

The correlation between x and y is positive correlation because it is a correlation where if one variable increases, the other also increases, and if one variable decreases, the other also decreases.

Test: Statistics- 1 - Question 8

Coefficient of correlation between the observations (1, 6) , (2 , 5) , (3 , 4) , (4 , 3) , (5 , 2) , (6 , 1) is

Test: Statistics- 1 - Question 9

If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρρsatisfies.

Test: Statistics- 1 - Question 10

For a moderately skewed distribution, quartile deviation and the standard deviation are related by

Detailed Solution for Test: Statistics- 1 - Question 10

The relationship between the mean, quartile and the standard deviation are as follows:
Mean Deviation is the mean of all the absolute deviations of a set of data.
Quartile deviation is the difference between “first and third quartiles” in any distribution.
Standard deviation measures the “dispersion of the data set” that is relative to its mean.
Mean Deviation = 4/5 × Quartile deviation
Standard Deviation = 3/2 × Quartile deviation

Test: Statistics- 1 - Question 11

Which one of the following average is most affected of extreme observations ?

Test: Statistics- 1 - Question 12

The H.M. of 4,8,16 is

Detailed Solution for Test: Statistics- 1 - Question 12

Test: Statistics- 1 - Question 13

The Mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0.

Test: Statistics- 1 - Question 14

The statistical method which helps us to estimate or predict the unknown value of one variable from the known value of the related variable is called

Test: Statistics- 1 - Question 15

The coefficient of correlation r satisfies

Test: Statistics- 1 - Question 16

S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is

Test: Statistics- 1 - Question 17

The most stable measure of central tendency is

Test: Statistics- 1 - Question 18

The mean weight of a group of 10 items is 28 and that of another group of n items is 35.The mean of combined group of 10 + n items is found to be 30. The value of n is

Test: Statistics- 1 - Question 19

The measure of variation which is least affected by extreme items is

Test: Statistics- 1 - Question 20

A group of 10 items has mean 6. If the mean of 4 of these items is 7.5, then the mean of the remaining items is

Detailed Solution for Test: Statistics- 1 - Question 20

Test: Statistics- 1 - Question 21

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

Detailed Solution for Test: Statistics- 1 - Question 21

Correlation coefficient = cov (x,y)/ (std deviation (x) ×std deviation (y))
Correlation coefficient  = 0.28
cov (x,y) = 7.6
variance of x is 9.
=> std deviation (x) = √variance  of X = √9 = 3
=>  0.28  = 7.6 / ( 3 * std deviation (y))
=> std deviation (y) = 7.6 / ( 3 * 0.28)
=> std deviation (y) = 9.05
standard deviation of Y series = 9.05

Test: Statistics- 1 - Question 22

The Q.D. of the daily wages (in Rs) of 7 persons given below: 12,7,15,10,17,19,25 is

Test: Statistics- 1 - Question 23

Which of the following is not a measure of central tendency :

Test: Statistics- 1 - Question 24

If the mean of numbers 27,31,89,107,156 is 82, then the mean of 130,126,68,50,1 is :

Test: Statistics- 1 - Question 25

If in moderately asymmetrical distribution mode and mean of the data are 6 μ and 9 μ respectively, then median is

Detailed Solution for Test: Statistics- 1 - Question 25

Median = [mode + 2(mean)]/3
= [6μ+2(9μ)]/3
= 24μ/3
= 8μ

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests