## 4. Mode

Mean and median are appropriate representations of the 'average' value for a set of observations of a continuous variable, that is one that can take any value. Neither is suited to category data, for instance where an event or response is scored on a scale from 'high' to 'low' or 'easy' to 'difficult'. Imagine ten observers are asked to rate a particular task on a five-point scale from 1 for 'very difficult' to 5 for 'very easy':

Observer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Rating | 5 | 3 | 5 | 2 | 3 | 4 | 5 | 4 | 2 | 5 |

Taking a mean of the ratings gives a value of 3.8, which is best expressed as 'just a bit short of easy'. Although this value is quite close to one of the category scores, it suggests a resolution that is inappropriate – the numerical values are simply labels and have no intrinsic significance. In this instance, the most suitable way to express a representative value is the mode. This is the category in which most observations or scores lie – in this case four of the ten observers rated the task as 'very easy' (score of 5).