9709 P51 - Nov 2020 - Q6
2488
The times, t minutes, taken by 150 students to complete a particular challenge are summarised in the following cumulative frequency table.
| Time taken (t minutes) | t ≤ 20 | t ≤ 30 | t ≤ 40 | t ≤ 60 | t ≤ 100 |
|---|---|---|---|---|---|
| Cumulative frequency | 12 | 48 | 106 | 134 | 150 |
(a) Draw a cumulative frequency graph to illustrate the data.
(b) 24% of the students take k minutes or longer to complete the challenge. Use your graph to estimate the value of k.
(c) Calculate estimates of the mean and the standard deviation of the time taken to complete the challenge.
