Seven students on an intramural team weigh 193 lb, 200 lb, 188 lb, 199 lb, 190 lb, 209 lb, and 193 lb. What is the standard deviation of the weights of these students? (Round to the nearest tenth.)

The standard deviation, an average measure of variability, for the student weights is approximately 6.2 lb. This figure is calculated based on the average student weight and deviations of individual weights from this average.

Explanation:

The standard deviation of a set of numbers essentially measures the average distance that each number is from the mean (average) of the set. In this case, the first step is to find the average weight of the seven students. You add all the weights together and divide by 7. The weights added together equal 1372 lb and dividing by 7 gives us an average weight of 196 lb. The second step is to calculate each student's deviation from this average (their weight minus the average) and square each result, then find the average of these squares. Lastly, you find the square root of this average. Using a calculator, the calculation ends up about 6.2 lb when rounded to the nearest tenth. Therefore, the standard deviation is approximately 6.2 lb.

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