Standard deviation (SD)

SD = Σ(x-x̄)² / n

For estimate of population,

SD = Σ(x-x̄)² / n-1 ( raw data)

SD = Σf(x-x̄)² / n-1 ( raw data) ( group data)

For practical purpose

SD = Σx²– (Σx)² / n-1 ( raw data)

SD = Σfx²– (Σfx)² / n-1 (group data)