NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Exercise

NCERT Solutions for Class 11 Maths Chapter 15 Statistics contain solutions for all Miscellaneous Exercise questions. Chapter 15 Statistics of Class 11 Maths is categorised under the CBSE Syllabus for the academic year 2022-23. Miscellaneous problems help students to learn and understand the difficulty level of questions asked from the chapter. Download the Maths NCERT Solutions of Class 11 to score well in the board exam. The students will also be able to gain more confidence by practising these solutions.

Download the 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, and 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

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

The mean of the n observation = x̅

The variance of the n observation = σ2

As we know,

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 observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (i) If the wrong item is omitted. (ii) If it is replaced by 12.

Solution:-

(i) If the 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 60

NCERT Soluitons for Class 11 Maths Chapter 15 Statistics Image 61

(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

The mean of Mathematics = 42

The standard deviation of Mathematics = 12

The mean of Physics = 32

The standard deviation of physics = 15

The mean of Chemistry = 40.9

The standard deviation of chemistry = 20

As we know,

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

The incorrect mean, (x̅) = 20

And the 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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