4 The weights, \(x \mathrm {~kg}\), of 120 students in a sports college are recorded. The results are summarised in the following table.
| Weight \(( x \mathrm {~kg} )\) | \(x \leqslant 40\) | \(x \leqslant 60\) | \(x \leqslant 65\) | \(x \leqslant 70\) | \(x \leqslant 85\) | \(x \leqslant 100\) |
| Cumulative frequency | 0 | 14 | 38 | 60 | 106 | 120 |
- Draw a cumulative frequency graph to represent this information.
\includegraphics[max width=\textwidth, alt={}, center]{82c36c11-878c-47d1-a07f-fbf8b2a22d97-06_1390_1389_660_418} - It is found that \(35 \%\) of the students weigh more than \(W \mathrm {~kg}\).
Use your graph to estimate the value of \(W\).
- Calculate estimates for the mean and standard deviation of the weights of the 120 students. [6]