7 The cumulative frequency graph below illustrates the distances that 176 children live from their primary school.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Distance from school}
\includegraphics[alt={},max width=\textwidth]{1ad9c390-b42f-47d8-86c5-f73a42d97721-04_1073_1571_580_340}
\end{figure}
- Use the graph to estimate, to the nearest 10 metres,
(A) the median distance from school,
(B) the lower quartile, upper quartile and interquartile range. - Draw a box and whisker plot to illustrate the data.
The graph on page 4 used the following grouped data.
| Distance (metres) | 200 | 400 | 600 | 800 | 1000 | 1200 |
| Cumulative frequency | 20 | 64 | 118 | 150 | 169 | 176 |
- Copy and complete the grouped frequency table below describing the same data.
| Distance ( \(d\) metres) | Frequency |
| \(0 < d \leqslant 200\) | 20 |
| \(200 < d \leqslant 400\) | |
| |
| |
| |
| |
- Hence estimate the mean distance these children live from school.
It is subsequently found that none of the 176 children lives within 100 metres of the school.
- Calculate the revised estimate of the mean distance.
- Describe what change needs to be made to the cumulative frequency graph.