Past variation gives information about future variation

In earlier pages of this section, we treated unexplained variation in data as 'noise' — a nuisance that cannot be avoided and that only serves to complicate the analysis of data.

This is not totally true. Variation can be interesting in its own right, especially when we are interested in predicting the future. If we can assume that there will be no systematic change to the process that generated the observed values in our data,

... the proportion of times that an event happened in the past indicates the chance that it will happen in the future.


Annual rainfall in Oxford

The table below shows the total rainfall in Oxford, England each year from 1963 to 2012.

Annual rainfall (mm)
639.9 494.6 577.7 723.6 530.5
418.5 783.8 608.7 703.5 727.4
658.4 538.4 662.0 683.4 504.7
751.2 509.2 704.1 457.6 765.1
700.0 710.6 595.6 599.6 753.9
813.1 576.8 571.1 765.3 820.9
609.2 751.9 598.8 736.7 620.5
641.6 634.3 473.0 826.7 603.7
740.6 682.9 526.8 677.0 480.9
575.7 654.5 795.6 813.5 984.4

If we assume that there is no climate change, the variation in these past rainfalls indicates the variation that we can expect in the future. For example, the rainfall was under 500 mm in 5 out of these 50 years, so we might expect such low rainfall in 10% of future years.


For countries that are susceptible to drought, the variability in past weather records might give information about:

This information can potentially help farmers decide which crops to plant and when to plant them.