# Australian Bureau of Statistics

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 Difference between mean, median and mode

Difference between mean, median and mode

The centre of a data set is important. It is often useful to know what the value is for most of the sample or population. In the ABS there are two main measures of central location: the mean and the median.

Mean
The mean, or average, is calculated by summing all of the observed values and dividing by the number of observations. The mean is the simplest way to summarise a single variable and it is generally the best measure of central location for purposes of statistical inference.

Median
The median is the middle value of a set of observations. There are as many observations above the median as there are below it. To find the median, observations must be arranged in order of value. Median is useful for variables such as age, income, turnover and housing prices.

Mode
The mode is the most commonly observed data item in a data set. A set of data can have more than one mode. The mode is useful when the most common item, characteristic or value of a data set is required.

 Example : Comparing the mean and the median If students attending a tutorial group were aged 18, 18, 19, 19, 21, 22 and 51, the mean age of the group would be 18 + 18 + 19 + 19 + 21 + 22 + 51 = 168 / 7 = 24 the median age of the group would be the middle value of 19. Which age best represents the average age of the group? In this case, the mean age is distorted by the presence of the mature age student. The median age would be a closer indication of the true average age of the tutorial group.

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