Formula and example
How it is calculated
Mean=Σx/n; population variance=Σ(x−mean)²/n. Binomial: P(X=k)=C(n,k)·p^k·(1−p)^(n−k).
Worked example
The list 2;4;4;4;5;5;7;9 has mean 5, median 4.5 and population standard deviation 2. For ten fair coin tosses, P(X=5) is 24.609375%.
Things to check
- List mode distinguishes population spread using divisor n from sample spread using divisor n−1.
- The binomial distribution assumes independent trials and a constant probability of success. For n=0, the number of successes is always 0.
Frequently asked questions
When should I look at the median?
The median describes the middle position in the sorted list. A few extreme values can shift the mean substantially, while usually affecting the median much less.