AVERAGE AND STANDARD DEVIATIONS

observation and are most frequently applied to temperature. Assume, for example, that the extreme highest temperature ever recorded at a particular station was 106°F and the lowest recorded was -15°F. These values are called the absolute maximum and absolute minimum, respectively. EXTREME The term extreme is applied to the highest and lowest values for a particular meteorological element occurring over a period of time. This period of time is usually a matter of months, seasons, or years. The term may be used for a calendar day only, for which it is particularly applicable to temperature. For example, the highest and lowest temperature readings for a particular day are considered the temperature extremes for that day. At times the term is applied to the average of the highest and lowest temperatures as mean monthly or mean annual extremes. RANGE Range is the difference between the highest and lowest values and reflects the extreme variations of these values. This statistic is not recommended for precise work, since it has a high variability. Range is related to the extreme values of record and can be useful in determining the extreme range for the records available. For example, if the highest temperature recorded yesterday was 76°F and the lowest was 41°F, then the range for the day was 35°F. FREQUENCY Frequency is defined as the number of times a certain value occurs within a specified period of time. When a large number of various values need to be presented, a condensed presentation of data may be obtained by means of a frequency distribution. MODE Mode is defined as the value occurring with the greatest frequency or the value about which the most cases occur. MEDIAN The median is the value at the midpoint in an array. In determining the median, all values are arranged in order of size. Rough estimates of the median may be obtained by taking the middle value of an ordered series; or, if there are two middle values, they may be averaged to obtain the median. The position of the median may be found by the following formula: Median =^n +1 2 where n is the number of items. The median is not widely used in climatological computations. However, some sources recommend the use of the median instead of the mean or average for some climatic elements to present more representative pictures of distribution and probability. A longer period of record might be required to formulate an accurate median. DEGREE-DAY A degree-day is the number of degrees the mean daily temperature is above or below a standard temperature base. The base temperature is usually 65°F; however, any temperature, Celsius or Fahrenheit, can be used as a base. There is one degree-day for each degree (°C or °F) of departure above or below the standard. Degree-days are accumulated over a season. At any point in the season, the total can be used as an index of past temperature effect upon some quantity, such as plant growth, fuel consumption, power output, etc. This concept was first used in connection with plant growth, which showed a relationship to cumulative temperature above a standard of 41°F. Degree-days are frequently applied to fuel and power consumption in the form of heating degree-days and cooling degree-days. AVERAGE AND STANDARD DEVIATIONS In the analysis of climatological data, it may be desirable to compute the deviation of all items from a central point. This can be obtained from a computation of either the mean (or average) deviation or the standard deviation. These are termed measures of dispersion and are used to determine whether the average is truly representative or to determine the extent to which data vary from the average. Average Deviation Average deviation is obtained by computing the arithmetic average of the deviations from an average of the data. First we obtain an average of the data, then the deviations of the individual items from this average are determined, and finally the arithmetic average of these 6-4