Types of variation

The table below summarises monthly rainfall data in a city over several years:

Rainfall
Month     Mean     Standard deviation
January 32.13 2.11
February 31.44 2.17
March 31.24 2.08
April 30.46 1.73
May 28.53 1.69
June 26.10 1.37
July 26.43 1.32
August 30.04 1.28
September    33.44 1.24
October 34.93 1.01
November 34.34 1.49
December 32.62 1.75
Overall 30.99 3.17

We can distinguish between three types of variation in the rainfalls:

Overall variation
Ignoring the months, the overall standard deviation is 3.17.
Unexplained variation
Variation within months is unexplained — it is unpredictable from available information. The standard deviations within months are between 1.01 and 2.17.
Explained variation
This is the difference between the overall and unexplained variation. (We do not give a numerical definition here.) Knowing the month would help to predict rainfall, so the month explains part of the variation in rainfalls.