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Class 11-commerce TR JAIN AND VK OHRI Solutions Statistics for Economics Chapter 9 - Measures of Central Tendency- Arithmetic Mean

Measures of Central Tendency- Arithmetic Mean Exercise 176

Solution SAQ 1

Solution SAQ 2

 

Solution SAQ 3

Students

Height (x)

d = X - A

A

155

-7

B

153

-9

C

168

6

D

160

-2

E

162 = A

0

F

166

4

G

164

2

H

180

18

I

157

-5

J

165

3

 

∑X = 1630

∑d = 10

 

Solution SAQ 4

 

Weight (X)

d = X - A

20

-30

28

-22

34

-16

39

-11

42

-8

50 = A

0

53

3

54

4

59

9

64

14

72

22

74

24

74

24

78

28

79

29

∑X = 820

∑d = 70

 

Measures of Central Tendency- Arithmetic Mean Exercise 177

Solution SAQ 5

 

Size (X)

Frequency

Deviation

d = X-A

fd 

30

2

5

10

29

4

4

16

28

5

3

15

27

3

2

6

26

2

1

2

25 = A

7

0

0

24

1

-1

-1

23

4

-2

-8

22

5

-3

-15

21

7

-4

-28

 

∑f = 40

 

fd = -3

 

Solution SAQ 6

 

Marks (X)

No. of Students (f)

fx 

15

8

120

20

4

80

22

7

154

23

3

69

27

8

216

35

7

245

18

5

90

 

∑f = 42

fX = 974

 

Solution SAQ 7

 

Age

 (X)

Mid-values (m)

People

 (f)

fm

10 - 20

15

30

450

20 - 30

25

32

800

30 - 40

35

15

525

40 - 50

45

12

540

50 - 60

55

9

495

 

 

∑f = 98

∑fm = 2810

 

Solution SAQ 8

 

Class Interval

Mid-values (m)

Frequency

 (f)

fm

10 - 20

15

4

60

20 - 40

30

10

300

40 - 70

55

26

1430

70 - 120

95

8

760

120 - 200

160

2

320

 

 

∑f = 50

∑fm = 2870

 

Solution SAQ 9

 

Class Interval

Mid- Value (m)

Frequency (f)

d = m-A

fd 

20 - 25

22.5

10

-15

-150

25 - 30

27.5

12

-10

-120

30 - 35

32.5

8

-5

-40

35 - 40

37.5 = A

20

0

0

40 - 45

42.5

11

5

55

45 - 50

47.5

4

10

40

50 - 55

52.5

5

15

75

 

 

∑f = 70

 

fd = -140

 

Solution SAQ 10

 

Items

(x)

Mid-Values

(m)

Frequency

(f)

d =

m-A

fd 

0 - 2

1

2

-4

-8

2 - 4

3

4

-2

-8

4 - 6

5 =A

6

0

0

6 - 8

7

8

2

16

8 - 10

9

10

4

40

 

 

∑f = 30

 

fd = 40

 

Solution SAQ 11

 

 

Thus, average mean of the runs is 33.875

Solution SAQ 12

Let first and the last class intervals be (0- 10) and (60 - 70) respectively.

 

Class Interval

Mid-Values (m)

Frequency (f)

fm

0 - 10

5

5

25

10 - 20

15

12

180

20 - 30

25

18

450

30 - 40

35

22

770

40 - 50

45

6

270

50 - 60

55

4

220

60 - 70

65

3

195

 

 

∑f = 70

∑fm = 2110

Solution SAQ 13

 

Solution SAQ 14

 

Measures of Central Tendency- Arithmetic Mean Exercise 178

Solution SAQ 15

 

Solution SAQ 16

 

Solution SAQ 17

 

Solution SAQ 18

 

Thus, average income of remaining families is Rs 3378.95.

Solution SAQ 19

 

 

Thus, missing frequency is 16.

Solution SAQ 20

 

Solution SAQ 21

 

Solution SAQ 22

 

Solution SAQ 23

 

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