Location - kopio
Mode (mo) is the most typical value of a variable. It may not be unique but can be used with all scales.
Median (md) is the middlemost value of an ordered data. If number of observations is even, then median is the average of two middlemost values. Median cannot be determined for variables in nominal scale.
Lower quartile (q1, Q1) is at 25% of an ordered data. Upper quartile (q3, Q3) is at 75% of an ordered data. Fractile is a general item for different percentages.
Statistics for location is easy to describe with Tukey's box-and-plot. For example, SPSS gives the observation number in a data for extremes and outliers. It helps in checking the values.
Figure 4.1 Box-plot
Mean is the most known statistical measure. It is very sensitive for extreme values. For that reason, it should not be informed alone like the above graph points out.
For discrete values, mean is solved with the formula
If some values are more important than the others, then values could be weighted:
Trimmed mean () may be used, if the data includes extremes. In that case, a % of obsevations are cut from both ends and the normal mean is solved for remaining values. In SPSS, cut is done at 5 %.
In windsorised mean (), the values are not cut but replaced with the nearest remaining value.
Figure 4.2 Location identifiers
The case b is the righthand tail and case c is lefthand tail. They may be problematic in tradional analysis.
SPSS gives the value automatically:
- if skewness > 0, it is the right hand tail
- if skewness < 0, it is the left hand tail
- if skewness is twice its standard error, then the distribution is not symmetric.