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Test: Variance And Standard Deviation - JEE MCQ


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10 Questions MCQ Test - Test: Variance And Standard Deviation

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Test: Variance And Standard Deviation - Question 1

Mean of the squares of the deviations from mean is called the:

Detailed Solution for Test: Variance And Standard Deviation - Question 1

Variance is the mean of the squares of the deviations from the mean. Variance is the square of standard deviation. Therefore any unit of a given set is converted into squares at the time of calculating the variance.

Test: Variance And Standard Deviation - Question 2

The variance of data: 0,10,20,30,40,50

Detailed Solution for Test: Variance And Standard Deviation - Question 2

Test: Variance And Standard Deviation - Question 3

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

Detailed Solution for Test: Variance And Standard Deviation - Question 3

sum of weights of 10 items = 280
sum of weights of n items = 35n
so, sum of weights of (10 + n) items = 280 + 35n
so ,mean = (280 + 35 n) / (10 + n)
30(10 + n) = 280 + 35n 
solving we get, n = 4

Test: Variance And Standard Deviation - Question 4

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

Test: Variance And Standard Deviation - Question 5

For a given data, the standard deviation is 20.If 3 is added to each observation , what is the new variance of the resulting observations?

Detailed Solution for Test: Variance And Standard Deviation - Question 5

If a three, is added to each number in a set of data, the mean will be increased by 3 and the standard deviation will be unaltered (since the spread of the data will be unchanged).
Hence, variance of the new data = 20

Test: Variance And Standard Deviation - Question 6

For a given data, the variance is 15. If each observation is multiplied by 2, what is the new variance of the resulting observations?

Detailed Solution for Test: Variance And Standard Deviation - Question 6

Variance = 15 
New variance = 22*15 
= 4*15 
= 60

Test: Variance And Standard Deviation - Question 7

The following values are calculated in respect of marks of the students of sections A and B of Class X:

The marks of which section have more variability?

Test: Variance And Standard Deviation - Question 8

If  is large, there is a ______ degree of dispersion.

Test: Variance And Standard Deviation - Question 9

The standard deviation for the following data:

Detailed Solution for Test: Variance And Standard Deviation - Question 9

Answer:  C
Solution:
Variance= [summation (y^2×f) /N] -[ summation (yf) /N]^2
=(296/25) -(0/25) ^2
=11.84
standard deviation=√11.84=3.12

Test: Variance And Standard Deviation - Question 10

The standard deviation of first 10 multiples of 4 is:

Detailed Solution for Test: Variance And Standard Deviation - Question 10

First 10 multiples of 4 are 4,8,12...40.
This is an A.P.
sum=n/2(a+l)
 = 10/2(4+40)
∴ sum=220.
Mean, u=sum/n
= 220/10 = 22
D1 = 4-22 = -18
D2 = 8-22 = -16
D3 = 12-22 = -10
D4 = 16- 22 = -8
Similarly we subtract multiple of 4 by 22 upto 10 terms we get 
-18, -14, -10, -8………...18
S.D. = σ2 = ∑(D2)/n
        =[ (-18)2 ,(-14)2, (-10)2, (-6)2 + (-2)2 +(6)2 + (10)2 + (14)2 + (18)2]/10
Solving this, we get
σ = 11.5​

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