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Question
Draw an ogive for the following :
| Marks (More than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative Frequency | 100 | 87 | 65 | 55 | 42 | 36 | 31 | 21 | 18 | 7 | 0 |
Solution
Steps :
1. Start with lower limits of class intervals and from cumulative frequency , subtract the frequency of each class to obtain c.f distribution .
2. Mark lower class limits along x-axis . 1 cm = 5 units
3. Mark cumulative frequencies along y-axis. 1 cm = 5 units
4. Plot points (x,f) where x is the lower limit of one class and f is the corresponding c.f. (0,100),(10,87),(20,65),(30,55),(40,42),(50,36),(60,31),(70,21),(80,18),(90,7),(100,0)
5. Join the points to get the ogive.
| Marks more than | Cumulative Frequency |
| 0 | 100 |
| 10 | 87 |
| 20 | 65 |
| 30 | 55 |
| 40 | 42 |
| 50 | 36 |
| 60 | 31 |
| 70 | 21 |
| 80 | 18 |
| 90 | 7 |
| 100 | 0 |
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The weight of 50 workers is given below:
| Weight in Kg | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 |
| No. of Workers | 4 | 7 | 11 | 14 | 6 | 5 | 3 |
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Draw an ogive by less than method for the following data:
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26 57 92 134 216 287 341 360 |
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| Class Interval | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 | 350-400 |
| Frequency | 10 | 13 | 17 | 12 | 10 | 8 |
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| Frequency | 28 | 23 | 15 | 20 | 14 |
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| No. of students | 8 | 22 | 48 | 60 | 75 |
Find the width of class 35 - 45.
Using a graph paper, drawn an Ogive for the following distribution which shows a record of the weight in kilograms of 200 students.
| Weight | Frequency |
| 40 - 45 | 5 |
| 45 - 50 | 17 |
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| 55 - 60 | 45 |
| 60 - 65 | 51 |
| 65 - 70 | 31 |
| 70 - 75 | 20 |
| 75 - 80 | 9 |
Use your ogive to estimate the following:
(i) The percentage of students weighing 55kg or more.
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The frequency distribution of scores obtained by 230 candidates in a medical entrance test is as ahead:
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| 400 - 450 | 20 |
| 450 - 500 | 35 |
| 500 - 550 | 40 |
| 550 - 600 | 32 |
| 600 - 650 | 24 |
| 650 - 700 | 27 |
| 700 - 750 | 18 |
| 750 - 800 | 34 |
| Total | 230 |
Draw a cummulative polygon (ogive) to represent the above data.
