There is an informative post on the website Hall of Record entitled “What is Normal”. I recommend Climate Science readers read the contributions on that weblog on this subject.
With respect to the term “normal, there is an issue as to what it means in climate science. In climate, “normal” is actually used to mean “average”, but it is misleading since a temperature that is above average is not abnormal unless it exceeds a threshold of deviation.
We discuss this issue in our paper
Pielke, R.A. and N. Waage, 1987: A definition of normal weather. Natl. Wea. Dig., 12, 20-22.
The abstract reads
“This paper clarifies the distinction between abnormal weather, and above and below average weather, using standard statistical analyses. Abnormal maximum and minimum temperatures are defined as requiring at least two standard deviations from the mean; otherwise even though they could be above or below average, the weather is still “normal”. July and January maximum and minimum temperatures for Denver, New York, Los Angeles, Miami and Bismarck are presented as examples of this analysis.”
Thus when the media or weather broadcasters state that the maximum (or minimum) temperature for a particular day is “above normal”, unless it is a large (e.g. greater than 2 sigma) deviation from the average maximum (or minimum) temperature, it is not really above normal.