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Question
The daily wages of 80 workers in a project are given below.
| Wages (in Rs.) |
400-450 | 450-500 | 500-550 | 550-600 | 600-650 | 650-700 | 700-750 |
| No. of workers |
2 | 6 | 12 | 18 | 24 | 13 | 5 |
Use a graph paper to draw an ogive for the above distribution. (Use a scale of 2 cm = Rs. 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate:
- the median wage of the workers.
- the lower quartile wage of workers.
- the numbers of workers who earn more than Rs. 625 daily.
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Solution
The cumulative frequency table of the given distribution is as follows:
| Wages (in Rs.) | Upper limit | No. of workers | Cumulative frequency |
| 400-450 | 450 | 2 | 2 |
| 450-500 | 500 | 6 | 8 |
| 500-550 | 550 | 12 | 20 |
| 550-600 | 600 | 18 | 38 |
| 600-650 | 650 | 24 | 62 |
| 650-700 | 700 | 13 | 75 |
| 700-750 | 750 | 5 | 80 |
The ogive is as follows:
Number of workers = n = 80
i. Median = `(n/2)^"th"` term = 40th term
Through mark 40 on the Y-axis, draw a horizontal line which meets the curve at point A.
Through point A, on the curve draw a vertical line which meets the X-axis at point B
The value of point B on the X-axis is the median, which is 605.
ii. Lower quartile (Q1) = `(80/4)^"th"` term = 20th term = 550
iii. Through mark of 625 on X-axis, draw a verticle line which meets the graph at point C.
Then through point C, draw a horizontal line which meets the Y-axis at the mark of 50.
Thus, the number of workers that earn more than Rs. 625 daily = 80 – 50 = 30.
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The marks obtained by 100 students in a Mathematics test are given below:
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Use a scale of 2 cm = 10 units on both axes.
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| Marks | No. of students |
| 600 - 640 | 16 |
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| 680 - 720 | 156 |
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| 760 - 800 | 172 |
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| 840 - 880 | 18 |
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| Production yield in kg per hectare: | 50 - 55 | 55 - 60 | 60 - 65 | 65 - 70 | 70 - 75 | 75 - 80 |
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Draw ‘less than’ ogive and ‘more than’ ogive.
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| Age in years (less than) | 10 | 20 | 30 | 40 | 50 | 60 | 70 |
| Cumulative frequency | 0 | 17 | 32 | 37 | 53 | 58 | 65 |
Construct a frequency distribution table for the following distributions:
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| Cumulative frequency | 100 | 87 | 65 | 55 | 42 | 36 | 31 | 21 | 18 | 7 | 0 |
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| Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
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| No. of people | 0 | 17 | 42 | 67 | 100 |
Find the width of class 35 - 45.
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| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 2 | 3 | 7 | 8 | 5 |
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| Class | 60-70 | 70-80 | 80-90 | 90-100 | Total |
| frequency | `"a"/2` | `(3"a")/2` | 2a | a | 50 |
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