6 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 \()\) | \(t \leqslant 20\) | \(t \leqslant 30\) | \(t \leqslant 40\) | \(t \leqslant 60\) | \(t \leqslant 100\) |
| Cumulative frequency | 12 | 48 | 106 | 134 | 150 |
- Draw a cumulative frequency graph to illustrate the data.
\includegraphics[max width=\textwidth, alt={}, center]{033ceb76-8fd4-4a89-ab05-5e20039d1c8d-08_1689_1195_744_516} - \(24 \%\) of the students take \(k\) minutes or longer to complete the challenge. Use your graph to estimate the value of \(k\).
- Calculate estimates of the mean and the standard deviation of the time taken to complete the challenge.