NCERT Solutions of chapter 15-Statistics class chapter 15-Statistics Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter-15 Statistics

Academic team of pw developed step by step NCERT Solutions for Class 11 Maths CChapter-15 Statistics Miscellaneous Exercise according to recommendations and Guideline of CBSE. You can download and share NCERT Solutions for Class 11 Maths.

NCERT Solutions for Class 11 Maths Miscellaneous Exercise

Question1. The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

Solution :
Let two required observations be x and y Then,

 

Question 2. The mean and variance of 7 observations are 8 and 16 respectively. If five of the observations are 2, 4, 10, 12, 14, find the remaining two observations.

Solution :
Let two required observations be x and y Then,

 

so, from eqn (i) ,we have

Question3. The mean and standard deviation of six observations are 8 and 4, respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

Solution :
 

Question4. Given that x̅ is the mean and σ² is the variance of n .observations x₁, x₂, …,x_n ..Prove that the mean and variance of the observations ax₁, ax₂, ax₃, …., ax_n are ax̅ and a²σ² respectively (a ≠ 0).

Solution :

From the question it is given that, n observations are x₁, x₂,…..x_n

Mean of the n observation = x̅

Variance of the n observation = σ²

As we know that,

 

Question5. The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

(i) if wrong item is omitted 

(ii) if it is replaced by 12.

Solution :

(i) If wrong item is omitted,

From the question it is given that,

The number of observations i.e. n = 20

The incorrect mean = 20

The incorrect standard deviation = 2

 

(ii) If it is replaced by 12,

From the question it is given that,

The number of incorrect sum observations i.e. n = 200

The correct sum of observations n = 200 – 8 + 12

n = 204

Then, correct mean = correct sum/20

= 204/20

= 10.2

 

 

Question6. The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:

Which of the three subjects shows the highest variability in marks and which shows the lowest?

Solution :

From the question it is given that,

Mean of Mathematics = 42

Standard deviation of Mathematics = 12

Mean of Physics = 32

Standard deviation of physics = 15

Mean of Chemistry = 40.9

Standard deviation of chemistry = 20

As we know that,

Therefore, Chemistry with highest C.V. shows highest variability and Mathematics with lowest C.V. shows lowest variability.

Question7. The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 12, 21 and 18. Find the mean and standard deviation if the incorrect observations are omitted.

Solution :

From the question it is given that,

The total number of observations (n) = 100

Incorrect mean, (x̅) = 20

And, Incorrect standard deviation (σ) = 3