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Question
The following table shows the distribution of the heights of a group of factory workers:
| Ht. (cm): | 150 – 155 | 155 – 160 | 160 – 165 | 165 – 170 | 170 – 175 | 175 – 180 | 180 – 185 |
| No. of workers: | 6 | 12 | 18 | 20 | 13 | 8 | 6 |
- Determine the cumulative frequencies.
- Draw the ‘less than’ cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.
Solution
| Height (in cm) | No. of workers | c.f. |
| 150 – 155 | 6 | 6 |
| 155 – 160 | 12 | 18 |
| 160 – 165 | 18 | 36 |
| 165 – 170 | 20 | 56 |
| 170 – 175 | 13 | 69 |
| 175 – 180 | 8 | 77 |
| 180 – 185 | 6 | 83 |
We plot the points (155, 6), (160, 18), (165, 36), (170, 56), (175, 69), (180, 77) and (185, 83) on the graph and join them in free hand to obtain an ogive.
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(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.
Use your Ogive to estimate :
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(ii) the upper quartile wage of the workers
(iii) the lower quartile wages of the workers
(iv) the percentage of workers who earn more than ₹ 45 a day.
The marks obtained by 120 students in a test are given below:
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| No. of Students | 5 | 9 | 16 | 22 | 26 | 18 | 11 | 6 | 4 | 3 |
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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 | 3 | 7 | 12 | 17 | 23 | 14 | 9 | 6 | 5 | 4 |
Draw an ogive for the given distribution on a graph sheet.
Use a scale of 2 cm = 10 units on both axes.
Use the ogive to estimate the :
- median.
- lower quartile.
- number of students who obtained more than 85% marks in the test.
- number of students who did not pass in the test if the pass percentage was 35.
