7. A doctor is investigating the correlation between blood protein, \(p\), and body mass index, \(b\).
He takes a random sample of 8 patients and the data are shown in the table below.
| Patient | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| \(b\) | 32 | 36 | 40 | 44 | 42 | 21 | 27 | 37 |
| \(p\) | 18 | 21 | 31 | 39 | 21 | 12 | 19 | 70 |
- Draw a scatter diagram of these data on the axes provided.
\includegraphics[max width=\textwidth, alt={}, center]{36cf6341-1957-45b9-9f7d-0914506f5919-13_938_673_785_614}
The doctor decides to leave out patient \(H\) from his calculations. - Give a reason for the doctor's decision.
For the 7 patients \(A , B , C , D , E , F\) and \(G\),
$$S _ { b p } = 369 , \quad S _ { p p } = 490 \text { and } S _ { b b } = 423 \frac { 5 } { 7 }$$
- Find the product moment correlation coefficient, \(r\), for these 7 patients.
- Without any further calculations, state how \(r\) would differ from your answer in part (c) if it was calculated for all 8 patients.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{36cf6341-1957-45b9-9f7d-0914506f5919-15_1322_1593_207_173}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The histogram in Figure 1 summarises the times, in minutes, that 200 people spent shopping in a supermarket. - Give a reason to justify the use of a histogram to represent these data.
Given that 40 people spent between 11 and 21 minutes shopping in the supermarket, estimate
- the number of people that spent between 18 and 25 minutes shopping in the supermarket,
- the median time spent shopping in the supermarket by these 200 people.
The mid-point of each bar is represented by \(x\) and the corresponding frequency by f .
- Show that \(\sum \mathrm { f } x = 6390\)
Given that \(\sum \mathrm { f } x ^ { 2 } = 238430\)
- for the data shown in the histogram, calculate estimates of
- the mean,
- the standard deviation.
A coefficient of skewness is given by \(\frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } }\)
- Calculate this coefficient of skewness for these data.
The manager of the supermarket decides to model these data with a normal distribution.
- Comment on the manager's decision. Give a justification for your answer.