CBSE (Commerce) Class 11CBSE
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NCERT solutions Mathematics Class 11 chapter 15 Statistics

Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 15 - Statistics

Pages 360 - 361

Find the mean deviation about the mean for the data

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

Q 1 | Page 360

Find the mean deviation about the mean for the data

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

Q 2 | Page 360

Find the mean deviation about the median for the data.

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

Q 3 | Page 360

Find the mean deviation about the median for the data

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

Q 4 | Page 360

Find the mean deviation about the mean for the data.

xi

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

Find the mean deviation about the mean for the data

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

 

Q 6 | 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

 

Q 7 | Page 360

Find the mean deviation about the median for the data

xi

15

21

27

30

35

fi

3

5

6

7

8

Q 8 | Page 360

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

Q 9 | 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

Q 10 | 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

Q 11 | 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

Q 12 | Page 361

Pages 371 - 372

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

Q 1 | Page 371

Find the mean and variance for the first natural numbers

Q 2 | Page 371

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

Q 3 | 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

Q 4 | 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

Q 5 | 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

 

Q 6 | 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

Q 7 | Page 371

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

Q 8 | 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

Q 9 | 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

Q 10 | Page 372

Pages 375 - 380

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

Q 1 | 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

Q 2 | 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?

Q 3 | Page 375

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

Q 3 | Page 380

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?

Q 4 | 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?

 
Q 5 | Page 376

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.

Q 1 | 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.

Q 2 | 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).

Q 4 | 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.

Q 5 | 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?

Q 6 | 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.

Q 7 | Page 380

NCERT Mathematics Class 11

Mathematics Textbook for Class 11
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