What is Standard Deviation?
Standard deviation is a statistical measurement that looks at how spread out a group of numbers is from the mean (average).
- A low standard deviation means most of the numbers are very close to the average. (e.g., The heights of adult golden retrievers).
- A high standard deviation means the numbers are spread out over a very wide range. (e.g., The salaries of people living in New York City).
Population vs. Sample: Which should I use?
The most common mistake people make when calculating variance and standard deviation is using the wrong formula. The math changes slightly depending on whether your data represents the entire group or just a small piece of the group.
Population (Divide by N)
Use this if your dataset includes every single member of the group you are studying.
Example: You are calculating the test scores of a class of 30 students, and you have the scores for all 30 students.
Sample (Divide by N-1)
Use this if your dataset is just a fraction of a larger group, and you are trying to estimate the whole group.
Example: You survey 1,000 random people to estimate the average income of a country of 300 million.
What is Variance?
Variance is the stepping stone to finding the standard deviation. It is the average of the squared differences from the Mean. Because the differences are squared, variance gives heavier weight to extreme outliers. To get the standard deviation from the variance, you simply take the square root of the variance.