Key takeaways
– Skewness quantifies asymmetry in a distribution: whether values pile up more on one side of the center and the tail stretches out on the other.
– Positive (right) skew: long right tail; mean > median. Negative (left) skew: long left tail; mean median > mode (typically).
– In a left-skewed distribution: mean < median median.
– Household income (right skew): Most households cluster in middle incomes; a relatively small set of very high incomes extend the right tail, making mean > median.
– Lifespan/age at death (left skew in many populations): Most people die at older ages; relatively fewer deaths at younger ages create a left tail.
– Equity returns: Many studies show stock markets can be negatively skewed over short periods (frequent small gains, occasional large drops). Individual firms’ equity could show different skew depending on firm-specific risk.
Where skewness is evident in the economy and what causes it
– Income and wealth data: Typically right-skewed because of compounding returns, top earners, and inequality.
– Insurance losses: Often right-skewed due to many small claims and occasional catastrophic claims.
– Asset returns: Skewness arises from leverage, option-like payoffs, jump risk, and structural asymmetries (e.g., limited upside vs. unlimited downside in some strategies, or vice versa).
– Firm sizes and sales: Often follow lognormal or power-law distributions, producing right skew.
Causes include multiplicative growth processes (which produce lognormal-like right skew), thresholds and floors (e.g., zero floor for prices or losses), asymmetrical decision rules, and rare shocks (jumps) that create heavy tails.
Is skewness normal?
Yes — skewness is common in economic and financial data. The normal distribution is symmetric and a useful benchmark, but many real-world variables deviate from normality. Expect skewness when outcomes are bounded on one side, when growth compounds multiplicatively, when rare extreme events exist, or when processes generate asymmetrical outcomes.
Practical example — roulette, simplified
– Bet $100 on one number out of 38:
• If you win: net payoff ≈ +$3,400 (payout minus stake)
• If you lose: net payoff = −$100
– Most spins are −$100; very rarely you get +$3,400. The distribution is right-skewed: the mean might be a small negative number (house edge), but the median is −$100 and skewness is strongly positive because of the rare large payoff.
Explain like I’m five
Imagine a playground seesaw where most kids sit on one side and a single very heavy kid sits far out on the other side. That one heavy kid tilts the seesaw a lot. Skewness is a way of saying “the seesaw is tipped more to this side because of a few extreme weights.” If the seesaw is balanced, skewness is zero.
Bottom line
Skewness is a simple but powerful diagnostic: it highlights directional imbalance in the distribution of observations and signals where extreme outcomes are more likely to occur. For analysts and investors, measuring and reacting to skewness leads to better understanding of tail risk and more appropriate modeling choices than relying on normality assumptions alone. Use visualization, appropriate skewness measures, statistical testing, and either transformations or asymmetric/tail-focused models to incorporate skewness into decision making.
Sources and further reading
– Investopedia, “Skewness”
– DeCarlo, L. T. (1997). On the meaning and use of kurtosis. Psychological Methods.
– Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice (for practical time-series modeling and distributions).
– Python SciPy stats documentation
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.