Summarizing Statistical Data
back to Statistics
In general, statistical data can be described as a list of subjects or Units and the data associated with each of them. Although most research uses many data types for each Unit, we will limit ourselves to just one data item each for this simple introduction.
We have two objectives for our summary:
- We want to choose a Statistic that shows how different Units seem similar. Statistical textbooks call the solution to this objective, a measure of Central Tendency.
- We want to choose another Statistic that shows how they differ. This kind of statistic is often called a measure of Statistical Variability.
When we are summarizing a quantity like length or weight or age, it is common to answer the first question with the Arithmetic Mean, the MediaN, or the MoDe. Sometimes, we choose specific values from the Cumulative Distribution Function called Quantiles.
The most common measures of variability for Quantitative Data are the Variance, its square root, the Standard Deviation, the Statistical Range, Interquartile Range, and the Absolute Deviation.