NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 15 Statistics, contains solutions for all Miscellaneous Exercise questions. Miscellaneous problems give proper exposure to the students. They will learn and understand the difficulty level of questions asked from the chapter. Download Maths NCERT Solutions of Class 11 now to score well. The students will also be able to gain more confidence by practicing these solutions.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Exercise

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Access Other Exercise Solutions of Class 11 Maths Chapter 15 Statistics

Exercise 15.1 Solutions : 12 Questions

Exercise 15.2 Solutions : 10 Questions

Exercise 15.3 Solutions : 5 Questions

Access NCERT Solutions for Class 11 Maths Chapter 15 Miscellaneous Exercise

1. 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:-

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 48

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 49

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 50

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:-

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 51

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 52

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 53

Hence, from equation (i) and (v) we have:

When x – y = 2 then x = 8 and y = 6

And, when x – y = – 2 then x = 6 and y = 8

∴ the remaining observations are 6 and 8

3. 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:-

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 54

We know that,

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 55

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 56

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

Solution:-

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

Mean of the n observation = x̅

Variance of the n observation = σ2

As we know that,

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 57

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 58

5. 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

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 59

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 61
NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 60

(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

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 62

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 63

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

Subject Mathematics Physics Chemistry
Mean 42 32 40.9
Standard deviation 12 15 20

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,

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 64

7. 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 21, 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

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 65

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 66

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 67

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