Draw an ogive for the following frequency distribution :
| Height (in cm) | No. of students |
|---|---|
| 150 - 160 | 8 |
| 160 - 170 | 3 |
| 170 - 180 | 4 |
| 180 - 190 | 10 |
| 190 - 200 | 2 |
Answer
To draw an ogive :
- The cumulative frequency table for the given continuous distribution is :
| Height (in cm) | No. of students | Cumulative frequency |
|---|---|---|
| 150 - 160 | 8 | 8 |
| 160 - 170 | 3 | 11 |
| 170 - 180 | 4 | 15 |
| 180 - 190 | 10 | 25 |
| 190 - 200 | 2 | 27 |
Since, the scale on x-axis starts at 150, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 150.
Take 2 cm along x-axis = 10 cm (height)
Take 1 cm along y-axis = 5 students
Plot the points (160, 8), (170, 11), (180, 15), (190, 25), (200, 27) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 150 - 160.Join these points by a freehand drawing.
The required ogive is shown in figure above.
Draw an ogive for the following frequency distribution :
| Class-intervals | Frequency |
|---|---|
| 1 - 10 | 3 |
| 11 - 20 | 5 |
| 21 - 30 | 8 |
| 31 - 40 | 7 |
| 41 - 50 | 6 |
| 51 - 60 | 2 |
Answer
To draw an ogive :
- The given frequency distribution is discontinuous, to convert it into continuous distribution,
Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2
The cumulative frequency table for the given data is :
| Classes before adjustment | Classes after adjustment | Frequency | Cumulative frequency |
|---|---|---|---|
| 1 - 10 | 0.5 - 10.5 | 3 | 3 |
| 11 - 20 | 10.5 - 20.5 | 5 | 8 |
| 21 - 30 | 20.5 - 30.5 | 8 | 16 |
| 31 - 40 | 30.5 - 40.5 | 7 | 23 |
| 41 - 50 | 40.5 - 50.5 | 6 | 29 |
| 51 - 60 | 50.5 - 60.5 | 2 | 31 |
Since, the scale on x-axis starts at 0.5, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 0.5
Take 2 cm along x-axis = 10
Take 1 cm along y-axis = 5
- Plot the points (10.5, 3), (20.5, 8), (30.5, 16), (40.5, 23), (50.5, 29), (60.5, 31) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 0.5 - 10.5
- Join these points by a freehand drawing.
The required ogive is shown in figure above.
Draw a cumulative frequency curve for the following data :
| Marks obtained | No. of students |
|---|---|
| 24 - 29 | 1 |
| 29 - 34 | 2 |
| 34 - 39 | 5 |
| 39 - 44 | 6 |
| 44 - 49 | 4 |
| 49 - 54 | 3 |
| 54 - 59 | 2 |
Answer
To draw an ogive :
- The cumulative frequency table for the given continuous distribution is :
| Marks obtained | No. of students | Cumulative frequency |
|---|---|---|
| 24 - 29 | 1 | 1 |
| 29 - 34 | 2 | 3 |
| 34 - 39 | 5 | 8 |
| 39 - 44 | 6 | 14 |
| 44 - 49 | 4 | 18 |
| 49 - 54 | 3 | 21 |
| 54 - 59 | 2 | 23 |
Since, the scale on x-axis starts at 24, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 24.
Take 1 cm along x-axis = 5 marks
Take 1 cm along y-axis = 5 (students)
- Plot the points (29, 1), (34, 3), (39, 8), (44, 14), (49, 18), (54, 21) and (59, 23) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 24 - 29.
- Join these points by a freehand drawing.
The required cumulative frequency curve is shown in figure above.