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Answer :
Final answer:
The standard deviation for the given precipitation data of U.S. cities comes out to be approximately 21.9 inches after calculating mean, finding deviations, squaring them, and finding square root of that variance.
Explanation:
To find the standard deviation for the given sample data, we first need to calculate the mean of the data. Add up all of the numbers and divide by the number of values in the data (6 in this case). The mean is approximately 23.42 inches. Next, find the deviation of each number in the set by subtracting the mean from each value and squaring the result. The deviations are (14.7-23.42)^2, (15.1-23.42)^2, (31.6-23.42)^2, (42.6-23.42)^2, (17.7-23.42)^2, and (18.8-23.42)^2. Add all the squared deviations together, this total is called the variance. The variance is approximately 480.15 square inches. Now, for the final step, take the square root of the variance to get the standard deviation. The standard deviation rounds to 21.9 inches to one more decimal place than was given in the original data.
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