Why we use standard deviation , not absolute deviation
We use standard deviation in finance and variance in calculating loss functions in machine learning. Why don't we use absolute deviation instead? In statistics, when you have large amount of sample data, you need some measures to interpret information from the data. Average/Mean is one such measure. This gives the figure, if you equally distribute the resource on each quantity, what each one will get. Mean helps when we compare two entities of different sizes. You can compare average salary of two companies, average cost of living in two cities, life expectancy of advanced and developing countries, per capita income of two countries etc. But mean does not give any idea on how data are dispersed. Income inequality in US is a hot economic /political issue. There are statistics to show how top 1 % of population gets lion's share of income and how bottom 20% makes quite less. To capture such deviations, we need to have some measures that convey how data are distributed. ( Gini inde...