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# Central tendency

The mean of data is obtained by adding all the values and dividing by the number of observations. Often, the mean is modelled as a balance point. This value is useful for predicting future results when there are no extreme values in the data set.

When extreme values are included in a data set, the median may be a more meaningful measure of centre. The May house prices in the table below show the mean can be greatly inflated by the sale of one million-dollar property. The mean house price varies by approximately $102 300 with the inclusion of the extreme value. It is not the best representation of the centre in this context. The median of the data is the middle value when numerical data have been written in ascending order. Half the observations are less than this value and half greater. The median house price for May is less likely to be affected by the sale of one expensive or inexpensive property. It only differs by$2500 with the inclusion of the extreme value.

 May house prices May house prices with an extreme value $385 000$385 000 $480 000$480 000 $475 000$475 000 $315 000$315 000 $560 000$560 000 $620 000$620 000 $470 000$470 000 $539 000$539 000 $445 000$445 000 $1 500 000 Mean:$476 555 Mean: $578 900 (differs by$102 345) Median: $475 000 Median:$477 500 (differs by \$2500)

## How long is a piece of string?

This investigation uses body-based measurements to estimate the length of a piece of string, using the mean arm span of students as an effective measure of centre.