11 The pre-release material contains information about the Median Income of Taxpayers and the Percentage of Pupils Achieving at Least 5 A*- C grades, including English and Maths, at the end of KS4 in different areas of London. Alex is investigating whether there is a relationship between median income and the percentage of pupils achieving at least 5 A* - C grades, including English and Maths, at the end of KS4. Alex decides to use the first 12 rows of data for 2014-5 from the pre-release data as a sample. The sample is shown in Fig. 11.1. \begin{table}[h] \end{table}

1. Explain whether the data in Fig. 11.1 is a simple random sample of the data for 2014-5.
2. The City of London is included in Alex's sample. Explain why Alex is not able to use the data for the City of London in this investigation. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Fig. 11.2 shows a scatter diagram showing Percentage of Pupils against Median Income for all of the areas of London for which data is available.} \includegraphics[alt={},max width=\textwidth]{e0b502a8-c742-4d78-993c-8c0c7329ec9c-09_716_1378_356_244}
   \end{figure} Fig. 11.2 Alex identifies some outliers.
3. On the copy of Fig. 11.2 in the Printed Answer Booklet, ring three of these outliers. Alex then discards all the outliers and uses the LINEST function on a spreadsheet to obtain the following model.
   \(\mathrm { P } = 0.0009049 \mathrm { M } + 37.38\),
   where \(P =\) percentage of pupils and \(M =\) median income.
4. Show that the model is a good fit for the data for Hackney.
5. Use the model to find an estimate of the value of \(P\) for City of London.
6. Give two reasons why this estimate may not be reliable. Alex states that more than 50\% of the pupils in London achieved at least a grade C at the end of KS4 in English and Maths in 2014-5.
7. Use the information in Fig. 11.2 together with your knowledge of the pre-release material to explain whether there is evidence to support this statement.