Measures of Location

When describing data with a few parameters, one can specify characteristic properties of the data distribution. Let us, for example, study a data set obtained from the measurement of the body weight of newly born babies:

We could observe that
 

• the average weight is 3.4 kg, or that
• 50 % of the babies weigh less than 3.3 kg, or that
• 95 % of the babies have a weight between 2.8 and 4.3 kg.

The first two statements specify in some manner the location of the maximum of the distribution, whereas the third line is a statement about the variability in the data.

In general, there are several measures of location, among them are
 

• the mean
• the median
• the mode

It is important to note that the mean is sensitive to outliers, whereas the median and the (1-p)-p-fractile are not. The median may remain almost constant if up to 50 % of the data is distorted. This behavior is often denoted as the robustness of the parameter. You may experiment with these three measures of location by starting the following  interactive example .