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Question
Draw an ogive to represent the following frequency distribution:
| Class-interval: | 0 - 4 | 5 - 9 | 10 - 14 | 15 - 19 | 20 - 24 |
| Frequency: | 2 | 6 | 10 | 5 | 3 |
Solution
Firstly, prepare the cumulative frequency table.
| Class Interval | No. of students | Less than | Cumulative frequency | Suitable points |
| 0-4 | 2 | 4 | 2 | (4, 2) |
| 5-9 | 6 | 9 | 8 | (9, 8) |
| 10-14 | 10 | 14 | 18 | (14, 18) |
| 15-19 | 5 | 19 | 23 | (19, 23) |
| 20-24 | 3 | 24 | 26 | (24, 26) |
Now, plot the less than ogive using the suitable points.
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RELATED QUESTIONS
The marks obtained by 100 students in a Mathematics test are given below:
| 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:
1) Median.
2) Lower quartile.
3) A number of students who obtained more than 85% marks in the test.
4) A number of students who did not pass in the test if the pass percentage was 35.
Draw an ogive by less than method for the following data:
| No. of rooms: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of houses: | 4 | 9 | 22 | 28 | 24 | 12 | 8 | 6 | 5 | 2 |
Draw an ogive for the following distributions:
| Marks obtained | less than 10 | less than 20 | less than 30 | less than 40 | less than 50 |
| No. of students | 8 | 25 | 38 | 50 | 67 |
Draw an ogive for the following distributions:
| 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:
| Marks (less than) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative frequency | 0 | 7 | 28 | 54 | 71 | 84 | 105 | 147 | 180 | 196 | 200 |
Construct a frequency distribution table for the following distributions:
| 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 |
Draw an ogive for the following :
| Class Interval | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 |
| Frequency | 28 | 23 | 15 | 20 | 14 |
Prepare the cumulative frequency (less than types) table from the following distribution table :
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 2 | 3 | 7 | 8 | 5 |
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 |
| 50 - 55 | 22 |
| 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.
(ii) The weight above which the heaviest 30% of the students fall.
(iii) The number of students who are:
(1) under-weight and
(2) over-weight, if 55·70 kg is considered as standard weight.
Cumulative frequency curve is also called ______.
