Mean, Variance and Standard Deviation 平均數、變異數、標準差

mean 平均數
standard deviation 標準差

population mean 母體平均數 μ = Σx_i /N = (x₁+x₂+...+x_N)/N, where i = 1 to N
population variance 母體變異數 σ² = Σ(x_i - μ)²/N, where i = 1 to N
population standard deviation 母體標準差 σ

sample mean 樣本平均數 x̄ = Σx_i /n = (x₁+x₂+...+x_n)/n, where i = 1 to n
sample variance 樣本變異數 s² = Σ(x_i - x̄)²/(n - 1), where i = 1 to n
sample standard deviation 樣本標準差 s

Note:
求標準差時只要將變異數開根號即可
σ² 和 s²的分母不同，母體變異數 σ² 的分母是N(或n)，樣本變異數 s²的分母則是n - 1

Excel Formulas:

mean - AVERAGE()

population variance - VAR.P()
sample variance - VAR.S()

population standard deviation - STDEV.P()
sample standard deviation - STDEV.S()

參考資料

Population Mean and Sample Mean

Sample Standard Deviation vs. Population Standard Deviation

統計學-李柏堅-第01章：標準差 (CUSTCourses影片)

Mathematical statistics with applications in R, Ramachandran & Tsokos, 2nd edition (2015), p26-27