Mathematics
Draw an ogive for the following frequency distribution:
| Marks obtained | No. of students |
|---|---|
| Less than 10 | 8 |
| Less than 20 | 23 |
| Less than 30 | 43 |
| Less than 40 | 50 |
| Less than 50 | 64 |
Answer
The cumulative frequency distribution :
| Marks obtained | Class interval | No. of students (Cumulative frequency) |
|---|---|---|
| Less than 10 | 0 - 10 | 8 |
| Less than 20 | 10 - 20 | 23 |
| Less than 30 | 20 - 30 | 43 |
| Less than 40 | 30 - 40 | 50 |
| Less than 50 | 40 - 50 | 64 |
Steps of construction of ogive:
Take 2 cm = 10 marks along x-axis.
Take 1 cm = 10 students along y-axis.
Ogive always starts from a point on x-axis representing the lower limit of the first class. Mark point (0, 0).
Take upper class limits along x-axis and corresponding cumulative frequencies along y-axis, mark the points (10, 8), (20, 23), (30, 43), (40, 50), (50, 64).
Join the points marked by a free hand curve.
The required ogive is shown in the below figure:
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