The average or arithmetic mean of the values of a set containing n elements is given by `A = (1/n)*sum_1^n t_n`. If the average temperature for a month is 75 F it is possible for the temperature on three days of the month to be 89 F, 88 F and...

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The average or arithmetic mean of the values of a set containing n elements is given by `A = (1/n)*sum_1^n t_n`. If the average temperature for a month is 75 F it is possible for the temperature on three days of the month to be 89 F, 88 F and 90 F. The low value of the average temperature indicates that on at least three other days the temperature was substantially lower than the average.

For a set with values that have a large variance, the arithmetic mean is not very significant. For example, the average temperature in a month can be 50 F though it is 0 F on half the days and 100 F on the others.

This makes it important to know the variance and standard deviation of the values before any inferences can be made given the average of a set of values. If the variance of the values is large it indicates the presence of values that are different from the mean by a large extent.