Averages

How do we calculate averages?

The draft Australian curriculum: mathematics indicates that by year 5, students should be able to understand and apply the concepts of median and mode. The median of a data set is the middle value, whereas the mode is the most frequently recorded value. These can largely be determined from visual representation of the data in graphs such as dot point graphs or leaf and stem plots. By year 7, students need to be able to calculate mean values from numerical data. The mean for a data set is obtained but summing the data values and dividing by the number of values recorded.

Example of averages calculation

Ten students scored 25%, 31%, 42%, 42%, 51%, 57%, 63%, 68%, 71% and 75% in a test.

Record this data in a stem and leaf plot

Data recorded in stem and leaf plot

Calculation of median

When there is an odd number of scores the median is the middle value. In this case there is an even number of scores with the middle two being 51 and 57. The median becomes (51+57) divided by two or 54.

Calculation of the mode

The mode or most frequent score is 42. It can be easily seen from the stem and leaf plot as it is the only score that is recorded twice. If all scores had only been recorded once there would be no value for the mode.

Calculation of the mean

Add the scores and divide them by the number of scores.

(25+31+42+42+51+57+63+68+71+75) divided by 10= 52.5