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T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode

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T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 237

Solution SAQ 1

Arranging data in ascending order:

Solution SAQ 2

Arranging data in ascending order:

 

Solution SAQ 3

 

 

Median value corresponds to the 37th item in the series. Thus, median value is 6 as it corresponds to cumulative frequency 40.

Solution SAQ 4

 

Solution SAQ 5

Arranging data in the ascending order:

S. No

Ages

1

2

2

9

3

10

4

11

5

13

6

14

7

16

8

18

 

N = 8

Solution SAQ 6

 

No. of person in a House

No. of House

(f)

Cumulative Frequency

(c.f.)

1

26

26

2

113

139

3

120

259

4

95

354

5

60

414

6

42

456

7

21

477

8

14

491

9

5

496

10

4

500

 

∑f =500

 

 

 

Median value corresponds to the 250.5th item in the series. Thus, median value is 3 as it corresponds to cumulative frequency 259.

Solution SAQ 7

 

Size

Frequency

(f)

Cumulative Frequency

(c.f.)

15

10

10

20

15

25

25

25

50

30

5

55

35

5

60

40

20

80

 

N = 80

 

 

 

Median value corresponds to the 40.5th item in the series. Thus, median value is 25 as it corresponds to cumulative frequency 50.

Solution SAQ 8

 

Marks

No. of Student

(f)

Cumulative Frequency

(c.f.)

0

4

4

5

6

10

10

15

25

15

5

30

20

8

38

25

12

50

30

28

78

35

14

92

40

3

95

45

5

100

 

N = 100

 

 

 

Median value corresponds to the 50.5th item in the series. Thus, median value is 30 as it corresponds to cumulative frequency 78.

Solution SAQ 9

 

Solution SAQ 10

Arranging the data in ascending order:

T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 238

Solution SAQ 11

 

Solution SAQ 12

Solution SAQ 13

 

Solution SAQ 14

 

Solution SAQ 15

Lower limits and upper limits of class intervals are calculated using the following formula.

  

where m is mid value and i is the difference between mid-values.

Solution SAQ 16

 

  

Solution SAQ 17

Mode of the given series is 75 as it has the highest frequency of 9.

Solution SAQ 18

 

Solution SAQ 19

 

  

Analysis Table

 

Column

Size of items containing maximum frequency

 

40

44

48

52

56

60 

64

68

72

76

I

 

 

 

 

 

 

 

 

 

 

II

 

 

 

 

 

 

 

 

 

 

III

 

 

 

 

 

 

 

 

 

 

IV

 

 

 

 

 

 

 

 

 

 

V

 

 

 

 

 

 

 

 

 

 

VI

 

 

 

 

 

 

 

 

 

 

Total

-

-

1

3

4

5

2

-

-

-

 

Mode is 60 as it repeats itself maximum number of times. 

T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 239

Solution SAQ 20

 

Solution SAQ 21

 

Solution SAQ 22

 

Wages

No. of Wages

0 - 10

15

10 - 20

35 - 15 =20

20 - 30

60 - 35 =25

30 - 40

84 - 60 =24

40 - 50

97 - 84 =12

50 - 60

127- 96 = 31

60 - 70

198 - 127= 71

70 - 80

250 - 198 = 52

By inspection, we can say that the modal class is 60 - 70 as it has the highest frequency of 71.

Solution SAQ 23

Mode of the given series is 5 as it has the highest frequency of 20 times.

Solution SAQ 24

 

No. of person per House

(X)

No. of House

(f)

fx

Cumulative Frequency (c.f.)

1

26

26

26

2

113

226

139

3

120

360

259

4

95

380

354

5

60

300

414

6

42

252

456

7

21

147

477

8

14

112

491

9

5

45

496

10

4

40

500

 

N=∑f = 500

∑fx = 1888

 

 

Solution SAQ 25

 

Marks

No. of Workers

(f)

Cumulative Frequency

(c.f.)

0 - 10

2

2

10 - 20

18

20

20 - 30

30

50

30 - 40

45

95

40 - 50

35

130

50 - 60

20

150

60 - 70

6

156

70 - 80

3

159

 

N = ∑f = 159

 

Solution SAQ 26

 

Age

No. of Student

(f)

Cumulative Frequency

(c.f)

20 - 25

50

50

25 - 30

70

120

30 - 35

100

220

35 - 40

180

400

40 - 45

150

550

45 - 50

120

670

50 - 55

70

740

55 - 60

60

800

 

∑f = 800

 

 

Solution SAQ 27

 

Marks

Mid Value

(m)

No. of Workers

 (f)

Cumulative Frequency (c.f.)

fm

0 - 10

5

5

5

25

10 - 20

15

7

12

105

20 - 30

25

15

27

375

30 - 40

35

25

52

875

40 - 50

45

20

72

900

50 - 60

55

15

87

825

60 - 70

65

8

95

520

70 - 80

75

5

100

375

 

 

N = ∑f =100

 

∑fm = 4000

 

 

Solution SAQ 28

Given:

Mode = 83

Mean = 92

Median =?

 

We know:

Mode = 3(Median) - 2(Mean)

83 = 3 (Median) - 2(92)

3 (Median) = 83 + 184

T.R. Jain and V.K. Ohri- Statistics for Economics Solution for Class 11 Commerce Statistics for Economics Chapter 10 - Measures of Central Tendency- Median and Mode Page/Excercise 240

Solution SAQ 29

Given:

Mean = 146

Median = 130

Mode =?

Mode = 3(Median) - 2(Mean)

Mode = 3(130) - 2(146)

Mode = 390 - 292

Solution SAQ 30

Given:

Mode = 63

Median = 77

Mean =?

We know:

Mode = 3(Median) - 2(Mean)

63 = 3 (77) - 2 (Mean)

2 (Mean) = 231 - 63 

Solution SAQ 31

 

Marks

Mid Point

(m)

Cumulative

Frequency

Frequency

fm

0 - 10

5

12

12

60

10 - 20

15

26

14

210

20 - 30

25

40

14

350

30 - 40

35

58

18

630

40 - 50

45

80

22

990

50 - 60

55

110

30

1650

60 - 70

65

138

28

1820

70 - 80

75

150

12

900

 

 

 

∑f = 150

∑fm = 6610

 

Text Book Solutions

CBSE XI Commerce - Statistics for Economics

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