5 [Figure 1, printed on the insert, is provided for use in this question.]
The table shows the times, in seconds, taken by a random sample of 10 boys from a junior swimming club to swim 50 metres freestyle and 50 metres backstroke.
| Boy | A | B | C | D | E | F | G | H | I | J |
| Freestyle ( \(\boldsymbol { x }\) seconds) | 30.2 | 32.8 | 25.1 | 31.8 | 31.2 | 35.6 | 32.4 | 38.0 | 36.1 | 34.1 |
| Backstroke ( \(y\) seconds) | 33.5 | 35.4 | 37.4 | 27.2 | 34.7 | 38.2 | 37.7 | 41.4 | 42.3 | 38.4 |
- On Figure 1, complete the scatter diagram for these data.
- Hence:
- give two distinct comments on what your scatter diagram reveals;
- state, without calculation, which of the following 3 values is most likely to be the value of the product moment correlation coefficient for the data in your scatter diagram.
$$0.912 \quad 0.088 \quad 0.462$$
- In the sample of 10 boys, one boy is a junior-champion freestyle swimmer and one boy is a junior-champion backstroke swimmer.
Identify the two most likely boys.
- Removing the data for the two boys whom you identified in part (c):
- calculate the value of the product moment correlation coefficient for the remaining 8 pairs of values of \(x\) and \(y\);
- comment, in context, on the value that you obtain.