5. In a survey unemployed people were asked how many months it had been, to the nearest month, since they were last employed on a full-time basis. The data collected is summarised in this stem and leaf diagram.
| Number of months | | (2 | 1 means 21 months) | Totals |
| 0 | | 11224446779 | (11) |
| 1 | | 02355689 | ( ) |
| 2 | 1568 | | ( ) |
| 3 | 079 | | ( ) |
| 4 | 5 | | ( ) |
| 5 | 27 | | (2) |
| 6 | 3 | | (1) |
| 7 | 0 | | (1) |
- Write down the values needed to complete the totals column on the stem and leaf diagram.
- State the mode of these data.
- 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 these data and suggest a reason for it.