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 (measures of central tendency), 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 quantiles 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 .