Temperature series (Figure 1) contain episodes of high and low values. Earlier we called these episodes seasons. About every 365 days or 1 year or fourth season the values in temperature series reach about the same magnitude. The time elapsed between two values of the same magnitude is defined as the period of a cycle. This temperature series is dominated by the annual cycle with a period of 1 year or 365 days.
The number indicating how many repetitions of a cycle occur per time interval is called the frequency. Figure 2 shows two sin series that are similar to temperature series. Series 1 has the same period (1 year) as the dominate period of the temperature series, whereas series two has a period of 2 years. Frequency of series 1 is two cycles per two years (1 cycle a year), and of series 2 one cycle per two years.
In statistics terms frequency has another meaning related to probability (so called Frequency Interpretation, Wilks, 1995). In this case frequency is interpreted as the number of observations in a certain range, category, or type.
Wilks, D.S.,1995. Statistical Methods in the Atmospheric Sciences. An Introduction. Academic Press, Inc., Pages 9-1 and 325- 333.