Answer: Choice D)
He needs to square each deviation in the numerator.
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Explanation:
The sample standard deviation involves these steps
- Find the sample mean xbar.
- Subtract the xbar value from each data point. This gets us the list of deviations or how far each person is from the mean.
- Square each difference in the previous step
- Add up the squares from step 3. This is referred to as the Sum of the Squared Errors (SSE)
- Divide the SSE over n-1. If Toby was doing a population standard deviation, then he'd divide over n instead of n-1. However in much of statistics, we don't know much about a population and instead rely on sample statistics.
- The result of step 5 gets the variance. Apply the square root to the variance to get the standard deviation.
The step 3 highlighted in bold is where Toby made an error. He subtracted xbar from each person correctly, but forgot to square those deviations. The squaring is done to ensure we don't have any negative deviations.
This is what his work should look like when calculating the sample standard deviation
[tex]s = \sqrt{\frac{(6-7)^2 + (5-7)^2 + (9-7)^2 + (8-7)^2}{3}}[/tex]
