What Is Skewness?
Let me explain skewness to you directly: it's a measure of asymmetry in a set of observations, where activity concentrates in one range and less in another. You see, a normal distribution has zero skewness and looks like a bell curve. Skewness shows how asymmetric your data is. If the distribution is right-skewed, the mean is higher than the median; if left-skewed, the mean is below the median.
Key Takeaways
Distributions can be positive and right-skewed or negative and left-skewed. A high skew might indicate outliers or kurtosis in your data. You can measure it using Pearson’s first and second coefficients of skewness.
Types of Skews
Negative or left-skewed distributions have a longer or fatter tail on the left side. Positive or right-skewed ones have that tail on the right. These show the direction or weight of the distribution. In a right-skewed setup, the mean is greater than the median because positive outliers pull it higher. For left-skewed, the mean is less than the median. A right-skewed distribution means the tail is more pronounced on the right, so most values are left of the mean, with extremes on the right. Negative skewness has the tail more on the left, most values on the right of the mean, and extremes further left. Remember, zero skew means symmetrical data, like a normal distribution, no matter the tail length.
Measuring Skewness
You can measure skewness with Pearson’s first and second coefficients. The first, or mode skewness, subtracts the mode from the mean and divides by the standard deviation. The second, median skewness, subtracts the median from the mean, multiplies by three, and divides by the standard deviation. Use the first if your data has a strong mode. If it's weak or has multiple modes, go with the second since it doesn't rely on the mode. Skewness tells you where outliers are, but not how many.
Formula for Pearson's Skewness
- Sk1 = (Mean - Mode) / Standard Deviation
- Sk2 = 3 * (Mean - Median) / Standard Deviation
- Where Sk1 is Pearson’s first coefficient, Sk2 the second, s is standard deviation, Mean is the average, Mo is mode, Md is median.
What Does Skewness Tell Investors?
As an investor, you should note skewness when judging return distributions because it considers extremes, not just the average, like kurtosis does. Short- and medium-term investors focus on these extremes since they might not hold positions long enough for averages to play out. You often use standard deviation for predictions, but it assumes normality. Since few returns are normal, skewness is better for basing predictions. Skewness risk is the higher chance of extreme data in skewed distributions. Financial models assuming normality will underestimate this risk if data is skewed, and more skew means less accurate models.
Example of Skewness
Take gambling as an example. Many games have high loss chances but rare huge payouts, creating right-skewed outcomes. In roulette, betting $100 on a single number: win $3,500 plus stake if it hits, lose $100 otherwise. Most spins lose, average loss around 5%, but rare wins make it heavily right-skewed.
Explain Like I'm Five
Skewness measures bias in numbers. Right skew: average above most data points. Left skew: average below most. Strong skew means a few extremes pull the average. No skew: even on both sides. Investors check skew for return likelihoods—some assets have positive expected returns but high skewness, meaning likely losses with small chance of big wins.
Where Is Skewness Evident in the Economy?
You see skewness in the stock market, often negatively skewed with small positives and large negatives. Individual firm equities tend left-skewed. Household income in the US is a classic right-skewed example.
What Causes Skewness?
Skewness happens when data condenses heavily in one range and less in another. Think Olympic long jumps: many longer jumps, few short ones, creating right-skew. It's the relationship and frequency of data points that cause it.
Is Skewness Normal?
Yes, skewness is common in data analysis; it's often just part of the set. For human lifespan, most die elderly, fewer young, so skewness is expected and normal.
The Bottom Line
Skewness statistically shows if a distribution is distorted or asymmetrical. Right-skewed: more high values. Left-skewed: tail more on left, more low values.
