The table shows the distribution of hours spent at work by the employees of a factory in a week.
| Time (in hours) | 20 – 29 | 30 – 39 | 40 – 49 | 50 – 59 | 60 – 69 | 70 – 79 |
| No of persons | 8 | 11 | 23 | 25 | 8 | 5 |
(a) Draw an ogive for the distribution.
(b) Using your graph, estimate the (i) lower quartile (ii) median (iii) 40th percentile (iv) number of employees that spent at least 50 hours 30 minutes at work.
Explanation
| Time in hours | No. of persons | Cum. freq | Class boundary |
| 20 – 29 | 8 | 8 | 19.5 – 29.5 |
| 30 – 39 | 11 | 19 | 29.5 – 39.5 |
| 40 – 49 | 23 | 42 | 39.5 – 49.5 |
| 50 – 59 | 25 | 67 | 49.5 – 59.5 |
| 60 – 69 | 8 | 75 | 59.5 – 69.5 |
| 70 – 79 | 5 | 80 | 69.5 – 79.5 |
(b) (i) Lower quartile = 40 hours
(ii) Median = 49 hours
(iii) 40th percentile = 45.5 hours
(iv) Employees that spent at least 50 hours 30 mins = 80 – 45 = 35