Step-by-step explanation:
we are creating the mean value of the squares of the differences of each data point to the mean value (variance), and then we pull the square root to bring the differences back to the same dimension as the basic data points.
and since we are dealing with the whole "population" of data points and not only with a sample of a much larger set of data points, that mean value of the differences is a true mean value (divide by n = the number of data points). if we would deal with a sample of a much larger population, we would divide by n-1.
so, how does this work in practice ?
let's go first for the given example :
2, 4, 6, 8.
the mean value is : (2+4+6+8)/4 = 20/4 = 5.
the variance (mean value of the squared differences of each data point to the mean value) :
((2-5)² + (4-5)² + (6-5)² + (8-5)²)/4 = (9+1+1+9)/4 = 20/4 = 5.
the standard deviation is the square root of the variance.
so,
SD = sqrt(5) = 2.236067977...
now for the given problem :
4, 8, 12, 20
the mean value is : (4+8+12+20)/4 = 44/4 = 11.
the variance (mean value of the squared differences of each data point to the mean value) :
((4-11)² + (8-11)² + (12-11)² + (20-11)²)/4 = (49+9+1+81)/4 = 140/4 = 35.
the standard deviation is the square root of the variance.
so,
SD = sqrt(35) = 5.916079783... ≈ 5.916
