While reading books on EDA(Exploratory Data Analysis), one of the interesting things was pseudo sigma. It’s a standard deviation like measure which is resistant to noises or outliers.

Simply put, given the first quartile H1 and the third quartile H3, pseudo sigma is (H3-H1)/1.35. Why? It’s because H1= μ – 0.675σ and H3 = μ + 0.675σ if X ∼N. Therefore, H3-H1=1.35σ, resulting in σ = (H3-H1)/1.35. We call H3-H1 as IQR(Inter Quartile Range).

Another way of computing sigma is using MAD(Median Absolute Deviations). This defines MAD = media(|x₁-m|, |x₂-m|, …, |x_n-m|) and MAD/0.675 = σ. That’s because, for m to be median, MAD should be σ / 1.4826 as below (See wikipedia):

Of course, we’re assuming X ∼N.