5. For a project, a student asked 40 people to draw two straight lines with what they thought was an angle of \(75 ^ { \circ }\) between them, using just a ruler and a pencil. She then measured the size of the angles that had been drawn and her data are summarised in this stem and leaf diagram.
| Angle | ( \(6 \mid 4\) means \(64 ^ { \circ }\) ) | Totals |
| 4 | 1 | (1) |
| 4 | | (0) |
| 5 | 024 | (3) |
| 5 | 589 | (3) |
| 6 | 11334 | (5) |
| 6 | 55789 | (5) |
| 7 | 011233444 | (9) |
| 7 | 5667799 | (7) |
| 8 | 01134 | (5) |
| 8 | 56 | (2) |
- Find the median and quartiles of these data.
Given that any values outside of the limits \(\mathrm { Q } _ { 1 } - 1.5 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)\) and \(\mathrm { Q } _ { 3 } + 1.5 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)\) are to be regarded as outliers,
- determine if there are any outliers in these data,
- draw a box plot representing these data on graph paper,
- describe the skewness of the distribution and suggest a reason for it.