Why is the standard deviation the most preferred measure of spread?

Answer 1

• perhaps mostly because it is most widely taught measure in undergraduate courses, and even in many graduate-level courses in statistics and inference
• it has an easily understood interpretation in terms of normal populations
• I suspect that many people find the mathematical operators involved in calculating it more familiar than those involved in calculing measures of spread based on L1 or other metrics
• statistical theory (and computer software) for ANOVA and other analogues of standard deviation has been much easier to create than that for L1 or other metrics
• there are classical results for the moments of distributions that do not involve absolute value or similar discontinuous functions