Sometimes data sets have to be summarised by a single value, usually called an average. There are three types of average measures commonly used: Mean Median Mode A Calculating each average measure Times (in minutes) taken to solve 'logic' question 27 members of a class were set a 'logic' 19 14 15 9 18 16 10 11 16 question and the times (in minutes) each 4 20 11 9 13 15 13 student took to solve it were noted. 12 2 17 14 10 11 10 12 1. The MEAN value of a set of data is sum of values number of values What is the mean (to 2 d.p.) of the times given in the table? 2. The MEDIAN is the middle value of an ordered set of data. (a) Write down the times in the table above in ascending order, i.e. smallest first. (b) How many values are there? (c) What is the median ? 3. The MODE is the value which occurs most often, i.e. the most popular (most common). What is the mode of the times in the table above? Which of the three measures do you think is most representative of the average time? Give your reasons. B Choosing which measure to use Dress sizes sold in one week 5 . In a clothes shop, the sizes of a particular dress 10 14 12 16 18 sold during one week were noted and are shown in 16 12 10 14 16 the table opposite. 16 14 18 8 14 (a) Find the mean, mode and median for this data. 12 16 10 10 16 16 18 14 16 8 (b) Which measure is of most use to the sales staff? Factory wages paid per week 6. The wages of factory employees are shown in the table. 10 are paid f120 35 are paid f140 (a) Find the mean, mode and median of the weekly wages. 25 are paid $160 (b) Which of these measures is the most useful? 30 are paid $180