WJEC Maths for AS: Applied sample

2 Data presentation and interpretation 34 Working out the mode The mode is the value(s) or class that occurs most often. The mode of 1, 1, 2, 9, 12, 1, 5 is 1 as it occurs the most often (i.e. three times). The modes of 1, 1, 2, 9, 12, 2, 5, 7 are 1 and 2 as both of these values occur the most often (i.e. twice). Note that you can have more than one mode so data can be multimodal. In some cases the mode of a set of data is not useful. For example, the mode of 1, 2, 3, 4, 5, 6 has no use because each value could be considered the mode. Modes are frequently used if there are one or two values that occur most often. Working out the median The median is the middle value when the data values are put in order of size. If there are an odd number of values, there will be a middle value and this will be the median. (e.g. for the data set 2, 4, 4, 5, 9 the median is 4) If there is an even number of values, there will be two values in the middle so the mean of these two values is the median. (e.g. for the data set 2, 4, 4, 5, 7, 9 the mean of the two middle values (i.e. 4 and 5) is found. This gives a median of 4.5.) Examples 1 Find the median of 12, 10, 1, 4, 10, 8, 3, 5 Answer 1 The data set in order of size is 1, 3, 4, 5, 8, 10, 10, 12 The two middle values are 5 and 8 so the median is the mean of these two values ( i.e. 5 + 82 = 6.5 ) . You can also use the following method: Find n which is the number of data values in the list ( n = 8 here) The median is at the n + 1 2 value. In this case n is 8 so 8 + 1 2 = 4.5th value which is the mean of the fourth and ϐifth values (i.e. 5 and 8) so the median is 5 + 8 2 = 6.5 2 The shoe sizes of a certain style of shoe in shop are as follows: 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 12 Find: (a) the mean size (b) the modal size (c) the median size.