Measures of Central Tendency

Question

When will the weighted arithmetic mean be less than the simple arithmetic mean?

Answer

The weighted arithmetic mean will be less than the simple arithmetic mean when items of small value are given greater weights and items of big values are given less weights.

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Some More Questions From Measures of Central Tendency Chapter

Comment on whether the following statements are True or False.

Following information pertains to the daily income of 150 families. Calculate the arithmetic means.

Income (in Rs.)

No. of Families

More than 75

More than 85

More than 95

More than 105

More than 115

More than 125

More than 135

More than 145

150

140

115

95

70

60

40

25

If the arithmetic mean of the data given below is 28, find (a) the missing frequency and (b) the median of the series.

Profit per retail shop (in Rs.)

Number of retail shops

0-10

10-20

20-30

30-40

40-50

50-60

12

18

27

17

6

The following series relates to the daily income of workers employed in a firm. Compute the (a) highest income of lowest 50% workers, (6) minimum income earned by the top 25% and (c) maximum income earned by lowest 25% workers.

Daily Income (in Rs.)

Number of Workers

10-14

15-19

20-24

25-29

30-34

35-39

5

10

15

20

10

5

The following table gives production yield in kg. per hectare of wheat of 150 arms in a village. Calculate the mean, median and mode production yield.

Production yield (kg. per hectare)

50-53

53-56

56-59

59-62

62-65

65-68

68-71

71-74

74-77

Number of farms

3

8

14

30

36

28

16

10

5

The size of land holdings of 380 families in a village is given below. Find the median size of land holdings.

Size of Land Holdings (in acres)

Number of families

less than 100

100-200

200-300

300-400

400 and above

40

89

148

64

39

What do you mean by 'Average'?

Pocket expenditures of 6 students are (Rs.) 6,12,18,24,30 and 36 respectively. Find out arithmetic mean.

Name various kinds of statistical averages?

Give formula of weighted averages.