Four steps to the standard deviation
Divide by n for a whole population, n − 1 for a sample
Use population when your numbers are everyone you care about: all 30 students in one class. Use sample when they stand in for a larger group: 30 survey answers from a city. A sample's own mean sits closer to its points than the true mean does, so dividing by n underestimates spread. Bessel's correction, dividing by n − 1, fixes that.
The gap shrinks fast as n grows. Slide to see it.
One outlier drags the mean; the median barely moves
The mode is the most frequent value; a dataset can have one, several or none. For skewed data, such as incomes with a few very high earners, the median usually describes the typical value better. Add an outlier to your own data to watch.
IQ scores are a mean and an SD
Modern IQ tests set the mean to 100 and the standard deviation to 15. Any score's z is (score − 100) ÷ 15, so 130 is z = 2, about the 98th percentile. On a normal curve about 68% fall within 1 SD, 95% within 2 and 99.7% within 3.