Understand standard deviation as a measure of spread and compare variability between data sets.
Standard deviation (sigma or s) measures how spread out data values are from the mean. - Small SD: data values are clustered near the mean - Large SD: data values are widely spread The SAT does not require you to calculate standard deviation by hand. Instead, you need to: 1. Understand what it means 2. Compare SD between data sets 3. Know how changes to data affect SD
Example: Which data set has a greater standard deviation? Set A: {48, 49, 50, 51, 52} Set B: {20, 35, 50, 65, 80}
Adding/subtracting a constant to every value: SD stays the same (shifting doesn't change spread). Multiplying/dividing every value by a constant k: SD is multiplied/divided by |k|. Adding an outlier: SD increases. Removing a value equal to the mean: SD decreases (you removed a 'centered' value).
Example: A data set has mean 50 and SD 8. If every value is multiplied by 3, then 10 is added, what are the new mean and SD?
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