6 For each of the Premiership football seasons 2004/05 and 2005/06, a count is made of the number of goals scored in each of the 380 matches. The results are shown in the table.
| \multirow{2}{*}{Number of goals scored in a match} | Number of matches |
| 2004/05 | 2005/06 |
| 0 | 30 | 32 |
| 1 | 79 | 82 |
| 2 | 99 | 95 |
| 3 | 68 | 78 |
| 4 | 60 | 48 |
| 5 | 24 | 30 |
| 6 | 11 | 9 |
| 7 | 6 | 6 |
| 8 | 2 | 0 |
| 9 | 1 | 0 |
| Total | 380 | 380 |
- For the number of goals scored in a match during the 2004/05 season:
- determine the median and the interquartile range;
- calculate the mean and the standard deviation.
- Two statistics students, Jole and Katie, independently analyse the data on the number of goals scored in a match during the 2005/06 season.
- Jole determines correctly that the median is 2 and that the interquartile range is also 2.
- Katie calculates correctly, to two decimal places, that the mean is 2.48 and that the standard deviation is 1.59 .
- Use your answers from part (a), together with Jole's and Katie's results, to compare briefly the two seasons with regard to the average and the spread of the number of goals scored in a match.
- Jole claims that Katie's results must be wrong as \(95 \%\) of values always lie within 2 standard deviations of the mean and \(( 2.48 - 2 \times 1.59 ) < 0\) which is nonsense.
Explain why Jole's claim is incorrect. (You are not expected to confirm Katie's results.)