8 In the 2001 census, the household size (the number of people living in each household) was recorded. The percentages of households of different sizes were then calculated. The table shows the percentages for two wards, Withington and Old Moat, in Manchester.
| \cline { 2 - 8 }
\multicolumn{1}{c|}{} | Household size |
| \cline { 2 - 8 }
\multicolumn{1}{c|}{} | 1 | 2 | 3 | 4 | 5 | 6 | 7 or more |
| Withington | 34.1 | 26.1 | 12.7 | 12.8 | 8.2 | 4.0 | 2.1 |
| Old Moat | 35.1 | 27.1 | 14.7 | 11.4 | 7.6 | 2.8 | 1.3 |
- Calculate the median and interquartile range of the household size for Withington.
- Making an appropriate assumption for the last class, which should be stated, calculate the mean and standard deviation of the household size for Withington. Give your answers to an appropriate degree of accuracy.
The corresponding results for Old Moat are as follows.
- State one advantage of using the median rather than the mean as a measure of the average household size.
- By comparing the values for Withington with those for Old Moat, explain briefly why the interquartile range may be less suitable than the standard deviation as a measure of the variation in household size.
- For one of the above wards, the value of Spearman's rank correlation coefficient between household size and percentage is - 1 . Without any calculation, state which ward this is. Explain your answer.