Statistics
Sample standard deviation
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The tourist bureau of the Caribbean Islands surveyed a sample of 5 United States tourists as they left to return home. The tourists were asked how many days they spent on their visits. Their responses were as follows.
\[
10,6,8,7,9
\]
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Find the standard deviation of this sample of numbers. Round your answer to two decimal places.
Answer
\(\boxed{1.41}\) is the standard deviation of this sample of numbers
Step 1 ：Calculate the mean of the data set: \(\frac{10 + 6 + 8 + 7 + 9}{5} = 8\)
Step 2 ：Find the squared differences from the mean: \((10-8)^2, (6-8)^2, (8-8)^2, (7-8)^2, (9-8)^2\) which are 4, 4, 0, 1, 1 respectively
Step 3 ：Calculate the variance by finding the average of these squared differences: \(\frac{4 + 4 + 0 + 1 + 1}{5} = 2\)
Step 4 ：Find the standard deviation by taking the square root of the variance: \(\sqrt{2} = 1.41\) (rounded to two decimal places)
Step 5 ：\(\boxed{1.41}\) is the standard deviation of this sample of numbers
