Suppose that you take n {\displaystyle n} samples X 1 , X 2 , … , X n {\displaystyle X_{1},X_{2},\ldots ,X_{n}} independently from the same distribution.
The statistic
X ¯ = X 1 + X 2 + ⋯ + X n n = 1 n ∑ i = 1 n X i {\displaystyle {\bar {X}}={\frac {X_{1}+X_{2}+\cdots +X_{n}}{n}}={\frac {1}{n}}\sum _{i=1}^{n}X_{i}}
is called a sample mean.
