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.
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:
Related Questions
Construct a frequency distribution table for the following distribution :
Marks (more than) Cumulative frequency 0 100 10 87 20 65 30 55 40 42 50 36 60 31 70 21 80 18 90 7 100 0 (a) Use the information given in the adjoining histogram to construct a frequency table.
(b) Use this table to construct an ogive.
Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
(i) Using the table, calculate the cumulative frequencies of workers.
(ii) Draw a cumulative frequency curve.
Wages (in ₹) No. of workers 6500 - 7000 10 7000 - 7500 18 7500 - 8000 22 8000 - 8500 25 8500 - 9000 17 9000 - 9500 10 9500 - 10000 8 Construct a frequency distribution table for the following distribution :
Marks (less than) Cumulative frequency 0 0 10 7 20 28 30 54 40 71 50 84 60 105 70 147 80 180 90 196 100 200