# Statistics - Online Test

Q1. A batsman scores runs in 10 innings as 38,70,48,34,42,55,63,46,54 and 44 , then the mean score is
Explaination / Solution:

Mean (x) =

= 494/10

= 49.4

Q2. The S.D. of the observations 22,26,28,20,24,30 is
Explaination / Solution:

Q3. If the angle between two lines of regression is  , then it represents
Explaination / Solution:

here

hence r = 0, therefore there is no linear correlation.

Q4. The two lines of regression are 2x - 7y + 6 = 0 and 7x – 2y +1 = 0. What is correlation coefficient between x and y ?
Explaination / Solution:

but sign of $\rho$ is same as the sign of

therefore,

Q5. The two lines of regression are x + 4y = 3 and 3x +y = 15 . value of x for y = 3 is
Explaination / Solution:

we have x + 4y = 3 and 3x + y = 15 as the lines of regression of y on x and x on y respectively.

therfore, for y = 3 the required line is x on y

so put y= 3 in 3x + y = 15

we get, x = 4

Q6. 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:
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

Q7. If x and y are related as y – 4x = 3, then the nature of correlation between x and y is
Explaination / Solution:

comparinf the given equation with ax + by + c= 0

a = -4, b =1 and c= -3

so ab < 0

hence,

so a perfect positive correlation.

Q8. Coefficient of correlation between the observations ( 1, 6 ) , ( 2 , 5 ) , ( 3 , 4) , ( 4 , 3 ) , ( 5 , 2 ) , ( 6 , 1 ) is
Explaination / Solution:

use,r(x,y)=1ni=1n(XiX¯)(YiY¯)1ni=1n(XiX¯)21ni=1n(YiY¯)2
Q9. If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρ satisfies.
Explaination / Solution:
No Explaination.

Q10. For a moderately skewed distribution, quartile deviation and the standard deviation are related by
Explaination / Solution:

its a standard result