Averages are used in everyday life to give us information about a set of numerical data, give an overview of the values seen and tell us the most common outcome. Range measures the spread of the data.
Each measure of central tendency interprets the data in a different way. It is important to be able to evaluate which average best represents the data, considering the type of information that is presented and the values given.
Question
From the 10 practice tests that Robert completed, he calculated:
Mean = 68
Mode = 65.5
Median = 64
Which measure would make his average score appear the highest?
The mean.
By choosing the average with the highest value, his average score appears higher than if he was to use the mode or median to represent the data.
Question
A boutique had daily sales of £326, £540, £385, £450, £2435, £459, £493 over the last week. Is the mean or median a more reliable measure of central tendency?
Mean = £726.86 (to nearest penny or two decimal places).
Median = £459.
As you can see, the mean isn’t representative of the data as it is higher than all but one of the values. This is because one value in the data is much larger than the rest. We say that £2435 is an outlier as it is much further away from the other values shown.
As a result, the median is a more reliable measure as the outlier does not affect it and the median is closer to all other numbers in the data.
Question
Contract Crunchers sell mobile phone contracts to 8 customers one morning. The monthly cost of these contracts are:
£45, £35, £35, £20, £34, £35, £35 and £35.
Does the mode describe this data well? Explain your answer.
Yes, as the mode £35 occurs 5 times out of 8 customers, it would be an appropriate value to represent the data.
£35 is the median as well as the mode, which strengthens the reliability of £35 as a suitable average to represent the data.
