Mathematics
(a) Use the information given in the adjoining histogram to construct a frequency table.
(b) Use this table to construct an ogive.
Statistics
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Answer
(a) The cumulative frequency table for above distribution is :
| Class interval | Frequency | Cumulative frequency |
|---|---|---|
| 8 - 12 | 9 | 9 |
| 12 - 16 | 16 | 25 |
| 16 - 20 | 22 | 47 |
| 20 - 24 | 18 | 65 |
| 24 - 28 | 12 | 77 |
| 28 - 32 | 4 | 81 |
(b) Steps of construction of ogive :
Since, the scale on x-axis starts at 8, a break (kink) is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 8.
Take 2 cm = 4 units along x-axis.
Take 1 cm = 10 units along y-axis.
Ogive always starts from a point on x-axis representing the lowest limit. Mark point (8, 0).
Take upper class limits along x-axis corresponding cumulative frequencies along y-axis, mark the points (12, 9), (16, 25), (20, 47), (24, 65), (28, 77) and (32, 81).
Join the points marked by a free hand curve.
The required ogive is shown in the adjoining figure.
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