4 On a certain day, the heights of 150 sunflower plants grown by children at a local school are measured, correct to the nearest cm . These heights are summarised in the following table.
| Height | | \(( \mathrm { cm } )\) |
| \(10 - 19\) | \(20 - 29\) | \(30 - 39\) | \(40 - 44\) | \(45 - 49\) | \(50 - 54\) | \(55 - 59\) |
| Frequency | 10 | 18 | 32 | 42 | 28 | 14 | 6 |
- Draw a cumulative frequency graph to illustrate the data.
\includegraphics[max width=\textwidth, alt={}, center]{915661eb-2544-4293-af72-608fedb43d70-06_1600_1301_760_383} - Use your graph to estimate the 30th percentile of the heights of the sunflower plants.
\includegraphics[max width=\textwidth, alt={}, center]{915661eb-2544-4293-af72-608fedb43d70-07_2723_35_101_20} - Calculate estimates for the mean and the standard deviation of the heights of the 150 sunflower plants.