The following data are the distances between a sample of 20 retail stores and a large distribution center. The distances are in miles.29; 38; 39; 40; 58; 67; 68; 69; 76; 81; 83; 95; 96; 96; 99; 106; 112; 127; 145; 150Find the value that is one standard deviation below the mean. (Round your answer to one decimal place.)
Question
The following data are the distances between a sample of 20 retail stores and a large distribution center. The distances are in miles.29; 38; 39; 40; 58; 67; 68; 69; 76; 81; 83; 95; 96; 96; 99; 106; 112; 127; 145; 150Find the value that is one standard deviation below the mean. (Round your answer to one decimal place.)
Solution
To find the value that is one standard deviation below the mean, we first need to calculate the mean (average) and the standard deviation of the data set.
Step 1: Calculate the mean (average) Add up all the distances and divide by the total number of distances.
29 + 38 + 39 + 40 + 58 + 67 + 68 + 69 + 76 + 81 + 83 + 95 + 96 + 96 + 99 + 106 + 112 + 127 + 145 + 150 = 1721
1721 ÷ 20 = 86.05
So, the mean (average) distance is 86.05 miles.
Step 2: Calculate the standard deviation First, subtract the mean from each distance, square the result, and then find the average of these squared differences.
[(29-86.05)^2 + (38-86.05)^2 + ... + (150-86.05)^2] ÷ 20
This gives us the variance. The standard deviation is the square root of the variance.
Let's say the standard deviation comes out to be 's' (you would need a calculator to compute this value).
Step 3: Subtract the standard deviation from the mean Finally, subtract the standard deviation from the mean to get the value that is one standard deviation below the mean.
86.05 - s
This is the final answer, rounded to one decimal place.
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