The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places.170, 160, 130, 165, 125Group of answer choices238.091420.9165168.8935133.23
Question
The top speeds for a sample of five new automobiles are listed below. Calculate the standard deviation of the speeds. Round to four decimal places.170, 160, 130, 165, 125Group of answer choices238.091420.9165168.8935133.23
Solution
To calculate the standard deviation of the speeds, follow these steps:
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Find the mean (average) of the speeds. Add all the speeds together and divide by the number of speeds.
(170 + 160 + 130 + 165 + 125) / 5 = 150
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Subtract the mean from each speed to get the deviation of each speed.
170 - 150 = 20 160 - 150 = 10 130 - 150 = -20 165 - 150 = 15 125 - 150 = -25
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Square each deviation.
20^2 = 400 10^2 = 100 -20^2 = 400 15^2 = 225 -25^2 = 625
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Find the mean of these squared deviations. This is called the variance.
(400 + 100 + 400 + 225 + 625) / 5 = 350
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Take the square root of the variance to get the standard deviation.
sqrt(350) = 18.7083
So, the standard deviation of the speeds is 18.7083, rounded to four decimal places.
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