12.5 a The first thing you need to do is to establish the data type. As it is numerical, you could theoretically use all three measures of central tendency and both the standard deviation and inter-quartile range. However, you would probably calculate the mean and perhaps the median as measures of central tendency and the standard deviation and perhaps the interquartile range as measures of dispersion. b The mean would be chosen because it includes all data values. The median might be chosen to represent the middle income over the 2004–12 period. The mode would be of little use for these data as each year has different income values. If you had chosen the mean you would probably choose the standard deviation, as this describes the dispersion of data values around the mean. The inter-quartile range is normally chosen where there are extreme data values that need to be ignored. This is not the case for these data.