Mathematics
The following table gives the weekly wages (in ₹) of workers in a factory :
Weekly wages (in ₹) | No. of workers |
---|---|
50 - 55 | 5 |
55 - 60 | 20 |
60 - 65 | 10 |
65 - 70 | 10 |
70 - 75 | 9 |
75 - 80 | 6 |
80 - 85 | 12 |
85 - 90 | 8 |
Calculate :
(i) the mean.
(ii) the modal class.
(iii) the number of workers getting weekly wages below ₹80.
(iv) the number of workers getting ₹65 or more but less than ₹85 as weekly wages.
Measures of Central Tendency
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Answer
We construct the following table :
Weekly wages (xi) | No. of workers (fi) | Class Mark (ui) | Cumulative frequency (C.F.) | fiui |
---|---|---|---|---|
50 - 55 | 5 | 52.5 | 5 | 262.5 |
55 - 60 | 20 | 57.5 | 25 | 1150 |
60 - 65 | 10 | 62.5 | 35 | 625 |
65 - 70 | 10 | 67.5 | 45 | 675 |
70 - 75 | 9 | 72.5 | 54 | 652.5 |
75 - 80 | 6 | 77.5 | 60 | 465 |
80 - 85 | 12 | 82.5 | 72 | 990 |
85 - 90 | 8 | 87.5 | 80 | 700 |
Total | 80 | 5520 |
(i) Mean = = 69.
Hence, mean = 69.
(ii) The class 55 - 60 has maximum frequency 20.
Hence, modal class is 55 - 60.
(iii) From table,
The number of workers getting weekly wages below ₹80 = 60.
(iv) From table,
The number of workers getting ₹65 or more but less than ₹85 as weekly wages = 72 - 35 = 37.
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