What Is Skewness?

A normal distribution exhibits zero skewness and is often shown as a 澳洲幸运5开奖号码历史查询:bell curve. Skewness is the degree of asymmetry observed in a set of data. A distribution is right-skewed if the mean is higher than the median, and left-skewed✱ if the𝓀 mean is below the median.

Types of Skews

Negative, or left-skewed, refers to a longer or fatter tail on the left side of the distribution, ꧂while positive, or right-skewed, refers to a longer or fatter tail on the right. These two skews show the direction or weight of the distribution.

The three probability distributions below are right-skewed to an increasing degree. The mean of positively skewed data will be greater ⭕than the median, because positive outliers pull the mean higher. In a left-skewed distribution, the mean o🉐f negatively skewed data will be less than the median.

A right-skewed or positive distribution me𝐆ans ✱its tail is more pronounced on the right side than on the left. Since the distribution is positive, the assumption is that its value is positive. As such, most of the values end up left of the mean. This means that the most extreme values are on the right side.

Negative or left-skewed means the tail is more pronounced on the left rather than the right. Most values are found on th♐e right side of the mean in negative skewness. As such, the most extreme values are found further to the left.

Measuring Skewness

Two methods to measure skewness include Pearson’s first and second coefficients of skewness. Pearson’s first coefficient of skewness, or Pearson's mode skewness, subtracts the mode from the mean and divides the difference by the 澳洲幸运5开奖号码历史查询:standard deviation.

Pearson’s secon🅘d coefficient of skewness, or Pearson median ske💞wness, subtracts the median from the mean, multiplies the difference by three, and divides the product by the standard deviation.

Formula for Pearson's Skewness

$\begin{aligned}&\qquad\qquad\qquad\quad\frac{Sk_1=\frac{\bar{X}-Mo}{s}}{Sk_2=\frac{3(X-Md)}{s}}\\&\textbf{where:}\\&Sk_1=\text{Pearson's first coefficient of skewness and } Sk_2\\&\qquad\quad\text{the second}\\&s=\text{The standard deviation for the sample}\\&\bar{X}=\text{Is the mean value}\\&Mo=\text{The modal (mode) value}\\&Md=\text{Is the median value}\end{aligned}$​Sk2​=s3(X−Md)​Sk1​=sXˉ−Mo​​where:Sk1​=Pearson’s first coeffici🐎ent of skewness and Sk2​the seconds=The&nbs𒐪p;standard🐬 deviation for the sampleXˉ=Is the mean valueMo=The modal (mode) valueMd=Is the median value​

Pearson’s first coefficient of skewness is used if the data exhibit a strong mode. Pearson's second coefficient may be preferable if the data have a weak mode or multiple modes, as it does not rely on the mode as a measure of central tendency.

What Does Skewness Tell Investors?

Investors note skewness when judging a return distribution because it, like kurtosis, considers the extremes of the data set rather than focusing solely on the average. 𓃲Short- and medium-term investors look at extremes because they are less likely to hold a position long enough to be confident that the average willꦅ work out.

Investors commonly use standard deviation to predict future returns,♋ but the standard deviation assumes a normal distribution. As few return distr▨ibutions appear normal, skewness is a better measure to base performance predictions.

Skewness risk is the increased risk of turning up a data point of high skewness in a skewed distribution. Many financial models that attempt to predict the future performance of an asset assume a normal distribution. If the data are skewed, this model will always underestimate skewness risk in its predictions. The more skewed the data, tꦜhe less accurate this financial model will be.

Example of Skewness

One common example of skewnessꦺ is gambling. Many gambling games involve a high chance of losses, but a rare chance of an extremely high payout.

Consider a single-number bet in a game of roulette: The player puts $100 on one of 38 numbers (European wheels have 37). If the ball lands on their number🧸, they get a payout of $3,500 plus their original stake. Otherwise, the pl🌠ayer loses $100.

Most spins lose money, but the "average" loss is only about 5%. Because of the rare chance of a high payout, the set of poss𒁃ible outcomes is heavily right-skewed.

Explain Like I'm Five

Skewness meaﷺsu🔥res the bias in a set of numbers. A right skew means that the average is above, or to the right, of most of the data points. A left skew means that the average is below, or to the left, of most of the data.

A strong s✨kew could mean a few extreme values that pull the average higher or lower. If there is no skew, the distribution of the numbers is the same on both sides of the average.

Investors study skew to understand the likely returns on their investments. Some assets have positive expected returns, but a high degree of skewness. That could mean a high probability that the investor would lose money, but a small probability of a high ret﷽urn.

The Bottom Line

Skewness is a statistical measure that shows whether a distribution is distorted or asymmetrical. If it is right-skewed, there are more high values than lower ones. If the opposite is true and the tail is more pronounced on the leℱft, then the skew is negative.