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What is the standard deviation of the annual rainfall in the town?
7.50 inches
11.78 inches
15.00 inches
9.25 inches
The correct answer is: 11.78 inches
To determine the standard deviation of annual rainfall in the town, one must understand the concept of standard deviation itself. Standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the individual values in a data set deviate from the mean (average) value. In this context, if the calculated standard deviation of the annual rainfall amounts to 11.78 inches, it signifies that the yearly rainfall amounts typically vary from the mean by approximately that amount. This suggests that while some years may experience significantly more or less rainfall, the overall variability is captured by this figure of 11.78 inches. To arrive at this answer, the twelve key steps typically utilized in calculating standard deviation would involve: 1. Calculating the mean annual rainfall. 2. Subtracting the mean from each year's rainfall to find the deviation of each value. 3. Squaring each of these deviations to remove negative values. 4. Summing the squared deviations. 5. Dividing by the number of data points to find the variance. 6. Taking the square root of the variance to arrive at the standard deviation. When compared against other potential answers, the value of 11.78 inches follows logical reasoning related to common ranges