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Question
Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
- Using the table, calculate the cumulative frequencies of workers.
- Draw a cumulative frequency curve.
Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y-axis.
| Wages (in ₹.) | 6500-7000 | 7000-7500 | 7500-8000 | 8000-8500 | 8500-9000 | 9000-9500 | 9500-10000 |
| No. of workers | 10 | 18 | 22 | 25 | 17 | 10 | 8 |
Solution
i.
| Wages | No. of workers | c.f. |
| 6500-7000 | 10 | 10 |
| 7000-7500 | 18 | 28 |
| 7500-8000 | 22 | 50 |
| 8000-8500 | 25 | 75 |
| 8500-9000 | 17 | 92 |
| 9000-9500 | 10 | 102 |
| 9500-10000 | 8 | 110 |
Total = 110
ii.
Now plot the points (7000, 10), (7500, 28), (8000, 50), (8500, 75), (9000, 92), (9500, 102) and (10000, 110) and join them to obtain an ogive.
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The marks obtained by 120 students in a test are given below:
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| No. of students | 5 | 10 | 14 | 21 | 25 | 34 | 36 | 27 | 16 | 12 |
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| 10 - 19 | 7 |
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| 60 - 69 | 37 |
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Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
(i) Using the table, calculate the cumulative frequency of workers.
(ii) Draw the cumulative frequency curve.
Use 2 cm = ₹500, starting the origin at ₹6,500 on X-axis, and 2 cm = 100 worker at they Y-axis.
(iii) Use your graph to write down the median wages in ₹.
| Wages in ₹ (CLass) |
No. of workers (frequency) | Cumulative frequency f(x) |
| 6500 - 7000 | 10 | - |
| 7000 - 7500 | 18 | - |
| 7500 - 8000 | 22 | - |
| 8000 - 8500 | 25 | - |
| 8500 - 9000 | 17 | - |
| 9000 - 9500 | 10 | - |
| 9500 - 10000 | 8 | - |
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| No. of Workers | 12 | 20 | 30 | 38 | 24 | 16 | 12 | 8 |
Using a graph paper, draw in Ogive for the above distribution.
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(i) the median wage of the workers.
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| Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| No. of Students | 5 | 9 | 16 | 22 | 26 | 18 | 11 | 6 | 4 | 3 |
Draw an ogive for the given distribution on a graph sheet.
Use suitable scale for ogive to estimate the following :
(i) the median.
(ii) The number of students who obtained more than 75% marks in the test.
