14 The pre-release material contains information concerning the median income of taxpayers in \(\pounds\) and the percentage of all pupils at the end of KS4 achieving 5 or more GCSEs at grade A*-C, including English and Maths, for different areas of London.
Some of the data for 2014/15 is shown in Fig. 14.1.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Fig. 14.1}
| Median Income of Taxpayers in £ | Percentage of Pupils Achieving 5 or more A*-C, including English and Maths |
| City of London | 61100 | \#N/A |
| Barking and Dagenham | 21800 | 54.0 |
| Barnet | 27100 | 70.1 |
| Bexley | 24400 | 55.0 |
| Brent | 22700 | 60.0 |
| Bromley | 28100 | 68.0 |
\end{table}
A student investigated whether there is any relationship between median income of taxpayers and percentage of pupils achieving 5 or more GCSEs at grade A*-C, including English and Maths.
- With reference to Fig. 14.1, explain how the data should be cleaned before any analysis can take place.
After the data was cleaned, the student used software to draw the scatter diagram shown in Fig. 14.2.
Scatter diagram to show percentage of pupils achieving 5 A*-C grades against median income of taxpayers
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Fig. 14.2}
\includegraphics[alt={},max width=\textwidth]{11788aaf-98fb-4a78-8a40-a40743b1fe15-10_574_1481_1900_241}
\end{figure}
The student calculated that the product moment correlation coefficient for these data is 0.3743 . - Give two reasons why it may not be appropriate to use a linear model for the relationship between median income of taxpayers in \(\pounds\) and the percentage of all pupils at the end of KS4 achieving 5 or more GCSEs at grade A*-C.
The student carried out some further analysis. The results are shown in Fig. 14.3.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Fig. 14.3}
| | median income of | | taxpayers in \(\pounds\) |
| | percentage of pupils | | achieving \(5 + \mathrm { A } ^ { * } - \mathrm { C }\) |
|
| mean | 27216 | 61.0 |
| standard deviation | 4177.5 | 5.32 |
- Use the information in Fig. 14.3 to determine the range of values of the median income of taxpayers in \(\pounds\) which are outliers.
- Use the information in Fig. 14.3 to determine the range of values of the percentage of all pupils at the end of KS4 achieving 5 or more GCSEs at grade A*-C which are outliers.
- On the copy of Fig. 14.2 in the Printed Answer Booklet, circle the three outliers identified by the student.
The student decided to remove these outliers and recalculate the product moment correlation coefficient.- Explain whether the new value of the product moment correlation coefficient would be between 0.3743 and 1 or between 0 and 0.3743 .