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Click here to Order your Radar Equipment Online 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 representa-tive 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 deviations is computed. The plus and minus signs are disregarded. The formula for computation of the average deviation is as follows:
Standard Deviation The standard deviation, like the average devia-tion, The formula for computing standard deviation is given as follows:
where d An example of the computations of average deviation and standard deviation is given in table 6-3-1 and in the following paragraphs. Suppose, on the basis of 10 years of data (1978-1987), you want to compute the average deviation of mean temperature and the standard deviation for the month of January. First arrange the data in tabular form (as in table 6-3-1), giving the year in the first column, the mean monthly temperature in the second column, the deviations from an arithmetic average of the mean temperature in the third column, and the devia-tions from the mean squared in the fourth column. Table 6-3-1.Computation of Average and Standard Deviation
To compute the average deviation: 1. Add all the temperatures in column 2 and 2. In column 3, compute the deviation from the mean or average determined in step 1. (The mean temperature for the 10-year period was 51F.) 3. Total column 3, disregarding the negative and positive signs, (Total is 26.) 4. Apply the formula for average deviation:
The average deviation of temperature during To compute the standard deviation: 1. Square the deviations from the mean (column 3). 2. Total these squared deviations. In this case, the total is 104. 3. Apply the formula for standard
deviation: The standard deviation of temperature for the |
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