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NCERT solution class 11 chapter 15 Statistics exercise 15.2 mathematics

EXERCISE 15.2


Page No 371:

Question 1:

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

Answer:

6, 7, 10, 12, 13, 4, 8, 12

Mean, 

The following table is obtained.

xi

6

–3

9

7

–2

4

10

–1

1

12

3

9

13

4

16

4

–5

25

8

–1

1

12

3

9

74

Question 2:

Find the mean and variance for the first natural numbers

Answer:

The mean of first n natural numbers is calculated as follows.

Question 3:

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

Answer:

The first 10 multiples of 3 are

3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Here, number of observations, = 10

The following table is obtained.

xi

3

–13.5

182.25

6

–10.5

110.25

9

–7.5

56.25

12

–4.5

20.25

15

–1.5

2.25

18

1.5

2.25

21

4.5

20.25

24

7.5

56.25

27

10.5

110.25

30

13.5

182.25

742.5

Question 4:

Find the mean and variance for the data

xi6101418242830
f i24712843

 

Answer:

The data is obtained in tabular form as follows.

xi

f i

fixi

6

2

12

–13

169

338

10

4

40

–9

81

324

14

7

98

–5

25

175

18

12

216

–1

1

12

24

8

192

5

25

200

28

4

112

9

81

324

30

3

90

11

121

363

40

760

1736

Here, N = 40, 

Question 5:

Find the mean and variance for the data

xi92939798102104109
f i3232633

 

Answer:

The data is obtained in tabular form as follows.

xi

f i

fixi

92

3

276

–8

64

192

93

2

186

–7

49

98

97

3

291

–3

9

27

98

2

196

–2

4

8

102

6

612

2

4

24

104

3

312

4

16

48

109

3

327

9

81

243

22

2200

640

Here, N = 22, 

Question 6:

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

xi606162636465666768
fi21122925121045

 

Answer:

The data is obtained in tabular form as follows.

xi

fi

yi2

fiyi

fiyi2

60

2

–4

16

–8

32

61

1

–3

9

–3

9

62

12

–2

4

–24

48

63

29

–1

1

–29

29

64

25

0

0

0

0

65

12

1

1

12

12

66

10

2

4

20

40

67

4

3

9

12

36

68

5

4

16

20

80

100

220

0

286

Mean, 

Question 7:

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

 

Answer:

Class

Frequency fi

Mid-point xi

yi2

fiyi

fiyi2

0-30

2

15

–3

9

–6

18

30-60

3

45

–2

4

–6

12

60-90

5

75

–1

1

–5

5

90-120

10

105

0

0

0

0

120-150

3

135

1

1

3

3

150-180

5

165

2

4

10

20

180-210

2

195

3

9

6

18

30

2

76

Mean, 

Page No 372:

Question 8:

Find the mean and variance for the following frequency distribution.

Classes0-1010-2020-3030-4040-50
Frequencies5815166

 

Answer:

Class

Frequency

fi

Mid-point xi

yi2

fiyi

fiyi2

0-10

5

5

–2

4

–10

20

10-20

8

15

–1

1

–8

8

20-30

15

25

0

0

0

0

30-40

16

35

1

1

16

16

40-50

6

45

2

4

12

24

50

10

68

Mean, 

Question 9:

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

Heightin 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

 

Answer:

Class Interval

Frequency fi

Mid-point xi

yi2

fiyi

fiyi2

70-75

3

72.5

–4

16

–12

48

75-80

4

77.5

–3

9

–12

36

80-85

7

82.5

–2

4

–14

28

85-90

7

87.5

–1

1

–7

7

90-95

15

92.5

0

0

0

0

95-100

9

97.5

1

1

9

9

100-105

6

102.5

2

4

12

24

105-110

6

107.5

3

9

18

54

110-115

3

112.5

4

16

12

48

60

6

254

Mean, 

Question 10:

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

 

Answer:

Class Interval

Frequency fi

Mid-point xi

fi2

fiyi

fiyi2

32.5-36.5

15

34.5

–2

4

–30

60

36.5-40.5

17

38.5

–1

1

–17

17

40.5-44.5

21

42.5

0

0

0

0

44.5-48.5

22

46.5

1

1

22

22

48.5-52.5

25

50.5

2

4

50

100

100

25

199

Here, N = 100, h = 4

Let the assumed mean, A, be 42.5.

Mean, 


 

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