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NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 5 - Measures of Central Tendency

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NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 5 - Measures of Central Tendency Page/Excercise 71

Solution 1

  1. Average size of readymade garments: Mode is a variable which is repeated the greatest number of times or occurs most frequently. So, this measure will be the most appropriate central tendency to determine the number of the average size of readymade garments. 
  2. Average intelligence of students in a class: Median can be calculated by sorting the data from smallest to largest and counting the middle value. So, this measure will be the most suitable central tendency to calculate the average intelligence of students in a class.
  3. Average production in a factory per shift: Arithmetic mean is the sum of the values of all observations divided by the number of observations. So, this measure will be the most appropriate central tendency to measure the average production in a factory per shift, i.e. it represents the central value or average production of the whole mass of production per shift. 
  4. Average wage in an industrial concern: Mean is the amount of wage secured by dividing the sum of wages of labourers by the number of labourers working in that industry. So, this measure will be the most appropriate central tendency to measure the average wage in an industrial concern.  
  5. When the sum of absolute deviations from average is least: The properties of arithmetic mean indicate that the sum of the deviations of the observations from their arithmetic mean is always zero. So, the arithmetic mean measure will be a more appropriate central tendency to measure the average when the sum of absolute deviations from average is least.
  6. When quantities of the variable are in ratios: Median can be calculated by sorting the data from smallest to largest and counting the middle value. If the quantities of the variable are in ratios, then the median measure can be obtained by taking the mean of the two observations and determining the position of the median at which the median lies. So, this measure will be a more appropriate central tendency to measure the quantities of variables given in ratios.
  7. In case of open-ended frequency distribution: Median will be more appropriate central tendency to measure open-ended frequency distribution. This measure of central tendency is not sensitive to all the values in the series and it focuses only on the values of the central items of the data. 

Solution 2(i)

The correct answer is option (b). Median can be calculated by sorting the data from smallest to largest and counting the middle value. So, this measure will be the most suitable average for qualitative measurement.  

NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 5 - Measures of Central Tendency Page/Excercise 72

Solution 2(ii)

The correct answer is option (c). One of the properties of arithmetic mean indicates that the average is affected by extreme values because any large value on either side can push it backward or forward.

Solution 2(iii)

The correct answer is option (b). One of the properties of arithmetic mean indicates that the sum of the deviations of a set of n values from A.M. is zero. However, the arithmetic mean is affected by extreme values.

Solution 3

  1. The statement is False. The properties of arithmetic mean indicate that the sum of the deviations of the observations from their arithmetic mean is always zero. 
  2. The statement is True. An average indicates only the behaviour of a particular series which is insufficient. The measure of dispersion reflects the quantum of variation in values. This implies that the measure of dispersion gives the extent to which values in a distribution differ from the average of the distribution.
  3. The statement is False. Arithmetic mean is not a positional value as it is based on all the observations. Median and mode are calculated by identifying the position at which they lie, i.e. the corresponding value at this position is the value of the median or mode.  
  4. The statement is True. Quartiles are measures which are divided into four equal portions. Upper quartile is the maximum which has 75% of the items of the distribution below it and 25% of the items above it.
  5. The statement is False. Median is unduly affected by extreme observations is not valid; the arithmetic mean is affected by extreme values, and any large value on either side can push it backward or forward.  

Solution 4

  1. Missing frequency: 

 

Profit per retail shop (in Rs) Class interval

No. of retail shops (f)

Mid-value (m)

  

fm

0-10

12

5

60

10-20

18

15

270

20-30

27

25

675

30-40

f1

35

35f1

40-50

17

45

765

50-60

6

55

330

 

∑f = 80 + f1

 

∑fm = 2100 + 35 f1

 

 

  1. Median of the series:

 

Profit per retail shop (in Rs)

Class interval

No. of retail shops Frequency (f)

Cumulative Frequency (cf)

0-10

12

12 = 12

10-20

18

12 + 18 = 30

20-30

27

30 + 27 = 57

30-40

20

57 + 20 = 77

40-50

17

77 + 17 = 94

50-60

6

94 + 6 = 100

Total

∑f = N = 100

 

 

  

Solution 5

 

Workers

Daily income (in Rs)

(X)

A

120

B

150

C

180

D

200

E

250

F

300

G

220

H

350

I

370

J

260

N = 10

∑ X = 2400

 

  

Solution 6

 

Since cumulative frequencies are given, convert into simple frequencies as presented below:

Income class interval

No. of families

Frequency (f)

Mid-value (m)

  

fm

75-85

150

150 - 140 = 10

80

800

85-95

140

140 - 115 = 25

90

2250

95-105

115

115 - 95 = 20

100

2000

105-115

95

95 - 70 = 25

110

2750

115-125

70

70 - 60 = 10

120

1200

125-135

60

60 - 40 = 20

130

2600

135-145

40

40 - 25 = 15

140

2100

145-155

25

25

150

3750

 

 

∑f = 150

 

∑fm = 17450

 

 

  

 

NCERT Solution for Class 11 Commerce Statistics for Economics Chapter 5 - Measures of Central Tendency Page/Excercise 73

Solution 7

Size of land holdings Class interval

No. of families

(f)

Cumulative frequency (cf)

0-100

40

40 = 40

100-200

89

40 + 89 = 129

200-300

148

129 + 148 = 277

300-400

64

277 + 64 = 341

400-500

39

341 + 39 = 380

 

∑f = 380

 

 

 

  

Solution 8

 

Daily Income (in Rs) Class interval

No. of worker

(f)

Cumulative frequency

(cf)

9.5-14.5

5

5 = 5

14.5-19.5

10

5 + 10 = 15

19.5-24.5

15

15 + 15 = 30

24.5-29.5

20

30 + 20 = 50

29.5-34.5

10

50 + 10 = 60

34.5-39.5

5

60 + 5 = 65

 

∑f = 65

 

 

  

 

  

Solution 9

 

  

 

iii. Mode

Grouping Table

Class interval

I

II

III

IV

V

VI

50-53

3

11

22

25

52

80

53-56

8

 

 

 

 

 

56-59

14

44

66

 

94

 

59-62

30

 

 

 

 

 

62-65

36

64

44

 

80

54

65-68

28

 

 

 

 

 

68-71

16

26

15

31

 

 

71-74

10

74-77

5

 

 

 

 

 

 

Analysis Table

  

  

Text Book Solutions

CBSE XI Commerce - Statistics for Economics

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