7. The following stem and leaf diagram shows the aptitude scores \(x\) obtained by all the applicants for a particular job.
| Aptitude score | 31 means 31 |
| 3 | 129 | (3) |
| 4 | 24689 | (5) |
| 5 | 1335679 | (7) |
| 6 | 0133356889 | (10) |
| 7 | 1222455568889 | (14) |
| 8 | 01235889 | (8) |
| 9 | 012 | (3) |
- Write down the modal aptitude score.
- Find the three quartiles for these data.
Outliers can be defined to be outside the limits \(\mathrm { Q } _ { 1 } - 1.0 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)\) and \(\mathrm { Q } _ { 3 } + 1.0 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)\).
- On a graph paper, draw a box plot to represent these data.
For these data, \(\Sigma x = 3363\) and \(\Sigma x ^ { 2 } = 238305\).
- Calculate, to 2 decimal places, the mean and the standard deviation for these data.
- Use two different methods to show that these data are negatively skewed.