Mathematics
The following table shows the distribution of the heights of a group of factory workers :
| Ht. (cm) | No. of workers |
|---|---|
| 150 - 155 | 6 |
| 155 - 160 | 12 |
| 160 - 165 | 18 |
| 165 - 170 | 20 |
| 170 - 175 | 13 |
| 175 - 180 | 8 |
| 180 - 185 | 6 |
(i) Determine the cumulative frequencies.
(ii) Draw the 'less than' cumulative frequency curve on graph paper.
Statistics
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Answer
(i) The cumulative frequency distribution table is as follows :
| Ht. (cm) | No. of workers | Cumulative frequency |
|---|---|---|
| 150 - 155 | 6 | 6 |
| 155 - 160 | 12 | 18 (6 + 12) |
| 160 - 165 | 18 | 36 (18 + 18) |
| 165 - 170 | 20 | 56 (36 + 20) |
| 170 - 175 | 13 | 69 (56 + 13) |
| 175 - 180 | 8 | 77 (69 + 8) |
| 180 - 185 | 6 | 83 (77 + 6) |
(ii) Steps for construction of 'less than' cumulative frequency curve :
Since, the scale on x-axis starts at 150, a break (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 = 5 cm.
Take 1 cm along y-axis = 10 workers.
Ogive always starts from a point on x-axis representing the lower limit of first class. Mark point (150, 0).
Take upper class limits along x-axis, corresponding cumulative frequencies along y-axis, mark the points (155, 6), (160, 18), (165, 36), (170, 56), (175, 69), (180, 77) and (185, 83).
Join the points marked by a free hand curve.
The required ogive is shown in the below figure:
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