Selina Solutions Concise Maths Class 10 Chapter 24 Measures of Central Tendency Exercise 24(B)

Continuing from the previous exercise, this exercise contains problems on finding the mean for grouped data (both continuous and discontinuous) by three methods. Direct method, short-cut method and step-deviation method are the three methods discussed under this exercise. The Selina Solutions for Class 10 Maths can be used by students for solving problems. Further, the solutions of the Concise Selina Solutions for Class 10 Maths Chapter 24 Measures of Central Tendency Exercise 24(B) are available in PDF format, provided in the link below.

Selina Solutions Concise Maths Class 10 Chapter 24 Measures of Central Tendency Exercise 24(B) Download PDF

 

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Access other exercises of Selina Solutions Concise Maths Class 10 Chapter 24 Measures of Central Tendency

Exercise 24(A) Solutions

Exercise 24(C) Solutions

Exercise 24(D) Solutions

Exercise 24(E) Solutions

Access Selina Solutions Concise Maths Class 10 Chapter 24 Measures of Central Tendency Exercise 24(B)

1. The following table gives the ages of 50 students of a class. Find the arithmetic mean of their ages.

Age – Years

16 – 18

18 – 20

20 – 22

22- 24

24-26

No. of Students

2

7

21

17

3

Solution:

Age in years

C.I.

xi

Number of students (fi)

xifi

16 – 18

17

2

34

18 – 20

19

7

133

20 – 22

21

21

441

22 – 24

23

17

391

24 – 26

25

3

75

Total

50

1074

Mean = ∑fi xi/ ∑fi = 1074/50 = 21.48

2. The following table gives the weekly wages of workers in a factory.

Weekly Wages (Rs)

No. of Workers

50-55

5

55-60

20

60-65

10

65-70

10

70-75

9

75-80

6

80-85

12

85-90

8

Calculate the mean by using:

(i) Direct Method

(ii) Short – Cut Method

Solution:

(i) Direct Method

Weekly Wages

(Rs)

Mid-Value

xi

No. of Workers (fi)

fixi

50-55

52.5

5

262.5

55-60

57.5

20

1150.0

60-65

62.5

10

625.0

65-70

67.5

10

675.0

70-75

72.5

9

652.5

75-80

77.5

6

465.0

80-85

82.5

12

990.0

85-90

87.5

8

700.0

Total

80

5520.00

Mean = ∑fi xi/ ∑fi = 5520/80 = 69

(ii) Short – cut method

Weekly wages (Rs)

No. of workers (fi)

Mid-value

xi

A = 72.5

di = x – A

fidi

50-55

5

52.5

-20

-100

55-60

20

57.5

-15

-300

60-65

10

62.5

-10

-100

65-70

10

67.5

-5

-50

70-75

9

A = 72.5

0

0

75-80

6

77.5

5

30

80-85

12

82.5

10

120

85-90

8

87.5

15

120

Total

80

-280

Here, A = 72.5

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 1

3. The following are the marks obtained by 70 boys in a class test:

Marks

No. of boys

30 – 40

10

40 – 50

12

50 – 60

14

60 – 70

12

70 – 80

9

80 – 90

7

90 – 100

6

Calculate the mean by:

(i) Short – cut method

(ii) Step – deviation method

Solution:

(i) Short – cut method

Marks

No. of boys (fi)

Mid-value xi

A = 65

di = x – A

fidi

30 – 40

10

35

-30

-300

40 – 50

12

45

-20

-240

50 – 60

14

55

-10

-140

60 – 70

12

A = 65

0

0

70 – 80

9

75

10

90

80 – 90

7

85

20

140

90 – 100

6

95

30

180

Total

70

-270

Here, A = 65

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 2

(ii) Step – deviation method

Marks

No. of boys (fi)

Mid-value xi

A = 65

ui = (xi – A)/ h

fiui

30 – 40

10

35

-3

-30

40 – 50

12

45

-2

-24

50 – 60

14

55

-1

-14

60 – 70

12

A = 65

0

0

70 – 80

9

75

1

9

80 – 90

7

85

2

14

90 – 100

6

95

3

18

Total

70

-27

Here, A = 65 and h = 10

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 3

4. Find mean by step – deviation method:

C. I.

63-70

70-77

77-84

84-91

91-98

98-105

105-112

Freq

9

13

27

38

32

16

15

Solution:

C. I.

Frequency (fi)

Mid-value xi

A = 87.50

ui = (xi – A)/ h

fiui

63 – 70

9

66.50

-3

-27

70 – 77

13

73.50

-2

-26

77 – 84

27

80.50

-1

-27

84 – 91

38

A = 87.50

0

0

91 – 98

32

94.50

1

32

98 – 105

16

101.50

2

32

105 – 112

15

108.50

3

45

Total

150

29

Here, A = 87.50 and h = 7

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 4

5. The mean of the following frequency distribution isSelina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 5. Find the value of ‘f’.

C. I.

0 – 10

10 – 20

20 – 30

30 – 40

40 – 50

freq

8

22

31

f

2

Solution:

Given,

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 6

C. I.

frequency

Mid-value (xi)

fixi

0-10

8

5

40

10-20

22

15

330

20-30

31

25

775

30-40

f

35

35f

40-50

2

45

90

Total

63 + f

1235 + 35f

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 7

9324 + 148f = 8645 + 245f

245f – 148f = 9324 – 8645

f = 679/97

Thus, f = 7

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