NCERT Solutions for Class 11 Maths Maths Chapter 15

Statistics Class 11

Chapter 15 Statistics Exercise 15.1, 15.2, 15.3, miscellaneous Solutions

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Exercise 15.1 : Solutions of Questions on Page Number : 360

Q1 :  

Find the mean deviation about the mean for the data

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


Answer :

The given data is

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

Mean of the data,

The deviations of the respective observations from the mean are

–6, – 3, –2, –1, 0, 2, 3, 7

The absolute values of the deviations, i.e., are

6, 3, 2, 1, 0, 2, 3, 7

The required mean deviation about the mean is

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Q2 :  

Find the mean deviation about the mean for the data

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


Answer :

The given data is

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

Mean of the given data,

The deviations of the respective observations from the mean are

–12, 20, –2, –10, –8, 5, 13, –4, 4, –6

The absolute values of the deviations, i.e. , are

12, 20, 2, 10, 8, 5, 13, 4, 4, 6

The required mean deviation about the mean is

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Q3 :  

Find the mean deviation about the median for the data.

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


Answer :

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Q4 :  

Find the mean deviation about the median for the data

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


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Q5 :  

Find the mean deviation about the mean for the data.

xi

5

10

15

20

25

fi

7

4

6

3

5


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Q6 :  

Find the mean deviation about the mean for the data

xi

10

30

50

70

90

fi

4

24

28

16

8


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Q7 :  

Find the mean deviation about the median for the data.

xi

5

7

9

10

12

15

fi

8

6

2

2

2

6


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Q8 :  

Find the mean deviation about the median for the data

xi

15

21

27

30

35

fi

3

5

6

7

8


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Q9 :  

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


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Q10 :  

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


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Q11 :  

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


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Exercise 15.2 : Solutions of Questions on Page Number : 371

Q1 :  

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


Answer :

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Q2 :  

Find the mean and variance for the first n natural numbers


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Q3 :  

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


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Q4 :  

Find the mean and variance for the data

xi

6

10

14

18

24

28

30

f i

2

4

7

12

8

4

3



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Q5 :  

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



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Q6 :  

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



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Q7 :  

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



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Q8 :  

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



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Q9 :  

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



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Q10 :  

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



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Exercise 15.3 : Solutions of Questions on Page Number : 375

Q1 :  

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


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Q2 :  

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


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Q3 :  

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


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Q4 :  

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?


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Q5 :  

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?


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Q6 :  

The sum and sum of squares corresponding to length x (in cm) and weight y

(in gm) of 50 plant products are given below:

Which is more varying, the length or weight?


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<< Previous Chapter 14 : Mathematical Reasoning Next Chapter 16 : Probability >>

Exercise Miscellaneous : Solutions of Questions on Page Number : 380

Q1 :  

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.


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Q2 :  

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.


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Q3 :  

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.


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Q4 :  

Given that 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 and a2 σ2, respectively (a ≠ 0).


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Q5 :  

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.


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Q6 :  

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?


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Q7 :  

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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<< Previous Chapter 14 : Mathematical Reasoning Next Chapter 16 : Probability >>

Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Statistics ( Exercise 15.1, 15.2, 15.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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