Sandeep Garg Solutions for Class 11 Economics Chapter 7 - Measures of Dispersion

Sandeep Garg Class 11 Economics Solutions Economics Chapter 7 – Measures of Dispersion are illustrated by the professional economic educator from the contemporary edition of Sandeep Garg Economics Class 11 textbook solutions.

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Sandeep Garg Solutions Class 11 – Chapter 7

Question 1

Evaluate the range and coefficient of the following series, that shows the monthly expenditure of seven students: 20, 32, 32, 49, 22, 31, 37

ANSWER:

Given:

Highest Value (H) =49

Lowest Value (L) =20

Range = Highest Value − Lowest Value

R= 49 − 20 = 29

Coefficient of Range = \(\frac{H-L}{H+L}\) = \(\frac{49-20}{49+20}\) = \(\frac{29}{69}\) = 0.42

Hence, the range is 29 and coefficient of range is 0.42

Question 2

Find range and coefficient of range from the weekly wage From the weekly wages of 8 labours of a workshop: 100, 120, 122, 138, 166, 185, 175, 155.

Answer:

Given:

Highest Value (H) = 185

Lowest Value (L) = 100

Range = Highest Value − Lowest Value

R= 185 − 100 = 85

Coefficient of Range = \(\frac{H-L}{H+L}\) = \(\frac{185 − 100}{185 + 100}\) = \(\frac{85}{285}\) = 0.29

Thus, range is 85 and coefficient of range is 0.29

Question 3

From the following data calculate range and coefficient of range:

Marks 15 25 35 45 55 65 75
No. of Studends 9 11 8 35 20 7 4

Answer:

Marks No. of Students
15

25

35

45

55

65

75

9

11

8

35

20

7

4

Highest value (H) = 75

Lowest value (L) = 15

Range = Highest value − Lowest value

or, R = 75 − 15= 60 marks

Coefficient of Range = \(\frac{H-L}{H+L}\) = \(\frac{ 75 − 15}{75 + 15}\) = \(\frac{60}{90}\) = 0.66

Hence, range is 60 and coefficient of range is 0.66

Question 4

Find out range and coefficient range.

Marks 20-30 30-40 40-50 50-60 60-70 70-80 80-90
No. of Students 8 10 9 30 25 6 5

Answer:

Marks No. of Students
20-30

30-40

40-50

50-60

60-70

70-80

80-90

8

10

9

30

25

6

5

Range = Upper limit of the highest class interval − Lower limit of the lowest class intervalor, Range = 90 − 20 = 70

Coefficient of Range = \(\frac{H-L}{H+L}\) = \(\frac{90 − 20}{90 + 20}\) = \(\frac{70}{110}\) = 0.63

Hence, the range is 70 marks and coefficient of range is 0.63

Question 5

Evaluate out range and coefficient of range of the marks.

Marks 5−9 10−14 15−19 20−24 25−29 30−34
No. Students 4 6 3 2 6 4

Answer:

To get the range and its coefficient, first we have to convert inclusive class intervals into exclusive class intervals.

Class Interval Exclusive Class Interval Frequency
5 − 9

10 −14

15 −19

20 −24

25 −29

30− 34

4.5 − 9.5

9.5 − 14.5

14.5 − 19.5

19.5 − 24.5

24.5 − 29.5

29.5 − 34.5

4

6

3

2

6

4

Range = Upper limit of the highest class interval − Lower limit of the lowest class intervalor, Range = 34.5 − 4.5 = 30

Coefficient of Range = \(\frac{H-L}{H+L}\) = \(\frac{34.5 − 4.5}{34.5 + 4.5}\) = \(\frac{30}{39}\) = 0.769

Hence, the range is 730 marks and coefficient of range is 0769

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