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NCERT solutions for Class 11 Mathematics chapter 15 - Statistics [Latest edition]

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Chapter 15: Statistics

Exercise 15.1Exercise 15.2Exercise 15.3Miscellaneous Exercise
Exercise 15.1 [Pages 360 - 361]

NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.1 [Pages 360 - 361]

Exercise 15.1 | Q 1 | Page 360

Find the mean deviation about the mean for the data

4, 7, 8, 9, 10, 12, 13, 17

Exercise 15.1 | Q 2 | Page 360

Find the mean deviation about the mean for the data

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Exercise 15.1 | Q 3 | Page 360

Find the mean deviation about the median for the data.

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Exercise 15.1 | Q 4 | Page 360

Find the mean deviation about the median for the data

36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Exercise 15.1 | Q 5 | Page 360

Find the mean deviation about the mean for the data.

xi

5 10 15 20 25
fi 7 4 6 3 5
Exercise 15.1 | Q 6 | Page 360

Find the mean deviation about the mean for the data

xi 10 30 50 70 90
fi 4 24 28 16 8

 

Exercise 15.1 | Q 7 | Page 360

Find the mean deviation about the median for the data.

xi

5

7

9

10

12

15

fi

8

6

2

2

2

6

 

Exercise 15.1 | Q 8 | Page 360

Find the mean deviation about the median for the data

xi

15

21

27

30

35

fi

3

5

6

7

8

Exercise 15.1 | Q 9 | Page 361

Find the mean deviation about the mean for the data.

Income per day

Number of persons

0-100

4

100-200

8

200-300

9

300-400

10

400-500

7

500-600

5

600-700

4

700-800

3

Exercise 15.1 | Q 10 | Page 361

Find the mean deviation about the mean for the data

Height in cms

Number of boys

95-105

9

105-115

13

115-125

26

125-135

30

135-145

12

145-155

10

Exercise 15.1 | Q 11 | Page 361

Find the mean deviation about median for the following data:

Marks

Number of girls

0-10

6

10-20

8

20-30

14

30-40

16

40-50

4

50-60

2

Exercise 15.1 | Q 12 | Page 361

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

Age

Number

16-20

5

21-25

6

26-30

12

31-35

14

36-40

26

41-45

12

46-50

16

51-55

9

Exercise 15.2 [Pages 371 - 372]

NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.2 [Pages 371 - 372]

Exercise 15.2 | Q 1 | Page 371

Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12

Exercise 15.2 | Q 2 | Page 371

Find the mean and variance for the first natural numbers

Exercise 15.2 | Q 3 | Page 371

Find the mean and variance for the first 10 multiples of 3

Exercise 15.2 | Q 4 | Page 371

Find the mean and variance for the data

xi

6

10

14

18

24

28

30

fi

2

4

7

12

8

4

3

Exercise 15.2 | Q 5 | Page 371

Find the mean and variance for the data

xi

92

93

97

98

102

104

109

f i

3

2

3

2

6

3

3

Exercise 15.2 | Q 6 | Page 371

Find the mean and standard deviation using short-cut method.

xi

60

61

62

63

64

65

66

67

68

fi

2

1

12

29

25

12

10

4

5

 

Exercise 15.2 | Q 7 | Page 371

Find the mean and variance for the following frequency distribution.

Classes

0-30

30-60

60-90

90-120

120-150

150-180

180-210

Frequencies

2

3

5

10

3

5

2

Exercise 15.2 | Q 8 | Page 372

Find the mean and variance for the following frequency distribution.

Classes

0-10

10-20

20-30

30-40

40-50

Frequencies

5

8

15

16

6

Exercise 15.2 | Q 9 | Page 372

Find the mean, variance and standard deviation using short-cut method

Height

in cms

No. of children

70-75

3

75-80

4

80-85

7

85-90

7

90-95

15

95-100

9

100-105

6

105-110

6

110-115

3

Exercise 15.2 | Q 10 | Page 372

The diameters of circles (in mm) drawn in a design are given below:

Diameters

No. of children

33-36

15

37-40

17

41-44

21

45-48

22

49-52

25

Exercise 15.3 [Pages 375 - 376]

NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Exercise 15.3 [Pages 375 - 376]

Exercise 15.3 | Q 1 | Page 375

From the data given below state which group is more variable, A or B?

Marks

10-20

20-30

30-40

40-50

50-60

60-70

70-80

Group A

9

17

32

33

40

10

9

Group B

10

20

30

25

43

15

7

Exercise 15.3 | Q 2 | Page 375

From the prices of shares X and Y below, find out which is more stable in value:

X

35

54

52

53

56

58

52

50

51

49

Y

108

107

105

105

106

107

104

103

104

101

Exercise 15.3 | Q 3 | Page 375

An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results::

 

Firm A

Firm B

No. of wage earners

586

648

Mean of monthly wages

Rs 5253

Rs 5253

Variance of the distribution of wages

100

121

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

Exercise 15.3 | Q 3 | Page 380

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

Exercise 15.3 | Q 4 | Page 376

The following is the record of goals scored by team A in a football session:

No. of goals scored

0

1

2

3

4

No. of matches

1

9

7

5

3

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Exercise 15.3 | Q 5 | Page 376

The sum and sum of squares corresponding to length (in cm) and weight (in gm) of 50 plant products are given below:

`sum_(i-1)^50 x_i = 212, sum_(i=1)^50 x_i^2 = 902.8, sum_(i=1)^50 y_i = 261, sum_(i = 1)^50 y_i^2 = 1457.6`

Which is more varying, the length or weight?

 
Miscellaneous Exercise [Page 380]

NCERT solutions for Class 11 Mathematics Chapter 15 Statistics Miscellaneous Exercise [Page 380]

Miscellaneous Exercise | Q 1 | Page 380

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.

Miscellaneous Exercise | Q 2 | Page 380

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.

Miscellaneous Exercise | Q 3. | Page 380

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.

Miscellaneous Exercise | Q 4 | Page 380

Given that  `barx` is the mean and σ2 is the variance of observations x1x2 … xn. Prove that the mean and variance of the observations ax1ax2ax3 …axare `abarx` and a2 σ2, respectively (a ≠ 0).

Miscellaneous Exercise | Q 5 | Page 380

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.

Miscellaneous Exercise | Q 6 | Page 380

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?

Miscellaneous Exercise | Q 7 | Page 380

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.

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Chapter 15: Statistics

Exercise 15.1Exercise 15.2Exercise 15.3Miscellaneous Exercise

NCERT solutions for Class 11 Mathematics chapter 15 - Statistics

NCERT solutions for Class 11 Mathematics chapter 15 (Statistics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics chapter 15 Statistics are Central Tendency - Median, Measures of Dispersion, Concept of Range, Mean Deviation, Introduction of Variance and Standard Deviation, Standard Deviation, Standard Deviation of a Discrete Frequency Distribution, Standard Deviation of a Continuous Frequency Distribution, Shortcut Method to Find Variance and Standard Deviation, Introduction of Analysis of Frequency Distributions, Comparison of Two Frequency Distributions with Same Mean, Statistics Concept, Central Tendency - Mean, Measures of Dispersion - Quartile Deviation, Standard Deviation - by Short Cut Method, Concept of Mode.

Using NCERT Class 11 solutions Statistics exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer NCERT Textbook Solutions to score more in exam.

Get the free view of chapter 15 Statistics Class 11 extra questions for Class 11 Mathematics and can use Shaalaa.com to keep it handy for your exam preparation

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