What is a Skewed Distribution? Definition, Types, 8 Facts

A skewed distribution in statistics is asymmetrical with data points clustered at one end, as opposed to being equally or normally distributed. Learn how data becomes skewed by investigating the concept, properties, and examples of skewed distributions.

Recognize whether data is favorably or negatively skewed, and discuss the responsibilities of the median, mean, and mode.

What is a Skewed Distribution?

When one tail is longer than the other, the distribution is skewed. The skewness of a distribution specifies its asymmetry. These distributions, unlike the well-known normal distribution with its bell-shaped curve, are asymmetric. The distribution’s two halves are not mirror images because the data are not evenly distributed on both sides of the distribution’s peak.

Asymmetrical distributions are a reality of life in a number of topic areas, despite the fact that they might make some individuals uncomfortable. There are rational explanations for why they arise, such as when natural restrictions distort the data away from the border. We will soon reach that point.

In this post, you will learn about left and right skewed distributions, the distinctions between histograms and boxplots, the ramifications of these distributions, why they exist, and how to analyze them.

Examples of a Skewed Distribution

In the recent two decades, beginning with the internet bubble of the late 1990s, the deviation from “normal” returns has been noted increasingly frequently. In reality, asset returns tend to get more right-skewed with time.

This volatility happened in response to significant events, such as the September 11 terrorist attacks, the fall of the housing bubble and ensuing financial crisis, and the years of quantitative easing (QE).

Typically, the broad stock market is seen as having a negatively skewed distribution. It is believed that the market yields a tiny profit more frequently than a significant loss. Nonetheless, research indicates that the equity of a certain company may be left-skewed.

A typical example of skewness is the distribution of household income in the United States, where people are less likely to achieve extremely high yearly incomes. Consider the household income figures for 2020 as an example.

The lowest percentile of income varied from $0 to $27,026, while the highest quintile of income went from $85,077 to $141,110. Due to the fact that the top quintile is more than twice as large as the lowest quintile, higher-income data points are more dispersed and result in a positively skewed distribution.

How to Tell if a Distribution is Left Skewed or Right Skewed

Let’s begin by comparing the properties of the symmetrical normal distribution to those of asymmetrical distributions.

Symmetric

The normal distribution contains a center peak where the majority of observations occur, and the chance of occurrences decreases proportionally in both positive and negative X-axis directions. Each section has the same amount of observations. In both tails, the probability of unusual values is equal.

What is a Skewed Distribution?

However, this is not the case for asymmetrical distributions, in which probability decline in one direction more slowly than the other. In other words, numbers farther from the peak are more likely to occur in one tail than the other. For this reason, you will hear about left and right skewed distributions, also known as negatively and positively skewed distributions.

Right Skewed (Positively Skewed)

Distributions that are right skewed have the long tail on the right side of the distribution. Also referred to be favourably biased by analysts. This situation develops because probability decline more gradually with increasing values. Therefore, extreme values distant from the peak are more prevalent on the high end than on the low.

Left-Skewed (Negatively Skewed)

Left skewed distributions occur when the long tail is on the left side of the distribution. Additionally, statisticians refer to them as negatively skewed. This circumstance develops because probability decline more gradually with decreasing values. Therefore, extreme values distant from the peak will occur more frequently on the low side than on the high side.

Important to remember is that the direction of the long tail establishes the skew, since it shows where the majority of exceptional values will be found.

What is a Negatively Skewed Distribution?

A negatively skewed (also known as left-skewed) distribution is a form of distribution in statistics in which more values are concentrated on the right side (tail) of the distribution graph while the left tail is longer.

In statistics, a negatively skewed distribution (also known as a left-skewed distribution) is a form of distribution in which more values are concentrated on the right side (tail) of the distribution graph, but the left tail of the distribution graph is longer.

Central Tendency Measures in Negatively Skewed Distributions

In contrast to properly distributed data, in which all measures of central tendency (mean, median, and mode) are equal, negatively skewed data have scattered measurements. The following inequality can be used to describe the overall connection between the central tendency measurements of a distribution with a negative skew.

Mode  >  Median  > Mean

The arithmetic mean of negatively skewed distributions is typically positioned to the left of the distribution’s peak, which is another crucial fact to remember about measures of central tendency. Despite the fact that the above given criteria are regarded as the basic rules for negatively skewed distributions, you may meet several outliers in the actual world.

Significant negative skewness in a distribution may preclude a complete statistical study. The excessive skewness of the data might lead to inaccurate conclusions from statistical testing. For this reason, the data undergoes a process of modification to approach a normal distribution. Statistical tests are often performed only after the data transformation is complete.

Examples of Left-Skewed Distributions

Less frequent than their right-handed counterparts, left-skewed distributions do exist. Frequently, they develop when values cannot exceed an upper limit and the majority of scores are close to that limit. The values cannot exceed the limit, but they can stretch quite far below the minimum, resulting in a negative skew.

What is a Skewed Distribution?

Left skewed distributions can occur, for instance, in the following situations:

  • Purity cannot exceed 100 percent, however extreme numbers are permitted on the low end.
  • The maximum score on a test cannot exceed 100 percent.
  • Deaths often occur between 70 and 80 years of age. It is feasible to live a bit longer, although extreme numbers are more likely to occur on the lower end of the spectrum.

Negatively Skewed Distribution in Finance

In finance, the skewness notion is used to analyze the distribution of investment returns. In spite of the fact that many theories and models of finance assume that the returns on securities follow a normal distribution, the returns are typically skewed.

The distribution’s negative skewness suggests that investors might anticipate several tiny wins and a few huge losses. In practice, many trading tactics adopted by traders are based on distributions with a negative skew.

Despite the fact that techniques based on negative skewness may generate steady earnings, investors and traders should be mindful of the possibility of substantial losses. Therefore, it is essential to accurately estimate the risks of trading methods and incorporate the skewness of the returns into the evaluation.

What is a Positively Skewed Distribution?

A positively skewed (or right-skewed) distribution is a form of distribution in statistics in which the majority of values cluster around the left tail of the distribution while the right tail is longer. Positively skewed distributions are diametrically opposed to negatively skewed distributions.

Central Tendency Measures in Positively Skewed Distributions

In contrast to normally distributed data, in which all measures of the central tendency (mean, median, and mode) are equal, the measurements of positively skewed data are spread. The following inequality can be used to describe the overall connection between the central tendency measurements in a distribution with a positive skew.

Mean  >  Median  >  Mode

In contrast to a negatively skewed distribution, in which the mean is located on the left from the peak of distribution, in a positively skewed distribution, the mean can be found on the right from the distribution’s peak. However, not all negatively skewed distributions follow the rules. You may encounter many exceptions in real life that violate the rules.

Since a high level of skewness can generate misleading results from statistical tests, the extreme positive skewness is not desirable for a distribution. In order to overcome such a problem, data transformation tools may be employed to make the skewed data closer to a normal distribution.

What is a Skewed Distribution?

The most common transformation for favorably skewed distributions is the log transformation. The log transformation requires the natural logarithm to be calculated for each value in the dataset. The strategy decreases the distribution’s skew. Typically, statistical tests are executed only after data transformation is complete.

Examples of Right-Skewed Distributions

Distributions with a right skew are the most prevalent type. These distributions are prevalent when there is a lower bound and the majority of values are close to it. Positively skewed values cannot go below this limit but can fall far from the peak on the high end.

Right skewed distributions can occur, for instance, in the following situations:

  • Time to failure cannot exceed zero, but there is no lower limit.
  • The minimum acceptable wait and response times are zero, but there are no higher restrictions.
  • The values of sales data cannot be less than zero, but they might be atypically huge.
  • Humans have a minimal sustainable weight, however high extreme levels are possible.
  • There is no such thing as a negative income, yet there are some exceptionally high earnings.

Examples of distributions with a right skew include income and wealth. Millionaires and billionaires stretch the right tail to extremely high levels. Moreover, the left tail cannot be negative. This circumstance results in a favorable skew. Because the mean overestimates the most prevalent values, publications usually refer to the median income.

2006 U.S. household income is the basis for these statistics. Observe how the mean is higher than the median.

Positively Skewed Distribution in Finance

The idea of skewness is applied to the investigation of the distribution of investment returns in the field of finance. Although many financial theories and models assume that the returns on securities follow a normal distribution, the returns are typically skewed in practice.

The positive skewness of a distribution suggests that investors might anticipate many small losses and a few number of huge wins. Positively skewed distributions of investment returns are often preferred by investors since there is a chance of achieving enormous profits that can compensate for the frequent minor losses.

What is a Skewed Distribution?

What Skewed Distributions Look Like in Graphs

In graphs, identifying asymmetric distributions is trivial. Simply locate the animal with the longest tail. Let’s examine this using histograms and boxplots. Here is how they appear in graphs.

Histograms

Below are two histograms displaying asymmetric distributions. Histograms facilitate the identification of longer tails. These positively and negatively skewed traits are also visible in the stem and leaf plot.

Boxplots

Boxplots require a closer inspection than histograms, although asymmetry can still be identified. I utilize the same data for both boxplots and histograms so that you can compare them.

When the box is centered around the median line and the upper and lower whiskers are roughly the same length, the distribution is symmetrical.

The distribution is right skewed when the median is closer to the box’s bottom values and the upper whisker is longer. Observe how the larger tail extends towards the higher values, rendering the distribution positively skewed.

A left-skewed distribution exists when the median is closer to the box’s upper values and the bottom whisker is longer. Observe how the larger tail stretches towards the lower values, resulting in a negative skew.

Skewed Distributions and the Mean, Median, and Mode

In a normal distribution and other symmetric distributions, the mean, median, and mode are all equal.

However, when there is an uneven distribution, the connection between these central tendency measurements is altered. The average is susceptible to outliers. In an asymmetrical distribution, the longer tail moves the mean away from the most frequent values.

The graphics below compare these measurements across several distributions.

Right skewed: The average exceeds the median. In a positively skewed distribution, the mean overestimates the most common values.

Left skewed: Median is greater than the mean. In a distribution with a negative skew, the mean understates the most prevalent values.

What is a Skewed Distribution?

In asymmetric distributions where the mean either overestimates or underestimates the most commonly occurring values, analysts typically employ the median. The median is a more solid statistic when extreme values are present.

Skewed Probability Distributions and Hypothesis Tests

When data are asymmetrical, a normal distribution cannot be used. You may need to conduct a distribution test to determine how your data are distributed. The probability distributions listed below are skewed:

  • Gamma
  • Exponential
  • Weibull
  • Lognormal
  • Beta

Learn more about why these distributions are asymmetrical and the traits they can model by clicking the links.

Numerous hypothesis tests presume that your data have a normal distribution. Nevertheless, many are valid with non-normal distributions when the sample size is sufficiently high. You have the central limit theorem to thank!

Conclusion

A skewed distribution in statistics is asymmetrical with data points clustered at one end, as opposed to being equally or normally distributed. Learn how data becomes skewed by investigating the concept, properties, and examples of skewed distributions. Recognize whether data is favorably or negatively skewed, and discuss the responsibilities of the median, mean, and mode.

A distribution is positively skewed if the scores are predominantly on the lower end of the scale and there are relatively few values on the upper end. Positively skewed data is sometimes referred to as being skewed to the right, as this is the direction of the chart’s “long tail end.” Let’s design a graph based on the MBA grads’ annual income data.

A distribution is negatively skewed if the majority of the scores are on the higher end of the scale and there are very few low values. Consider the chart depicting the amount of job applications each graduate submitted before landing their present position.

FAQ

A skewed distribution is neither symmetric nor normal because the data values trail off more sharply on one side than on the other. In business, you often find skewness in data sets that represent sizes using positive numbers (eg, sales or assets).
A distribution is skewed if one of its tails is longer than the other. The first distribution shown has a positive skew. This means that it has a long tail in the positive direction. The distribution below it has a negative skew since it has a long tail in the negative direction.
For example, take the numbers 1,2, and 3. They are evenly spaced, with 2 as the mean (1 + 2 + 3 / 3 = 6 / 3 = 2). If you add a number to the far left (think in terms of adding a value to the number line), the distribution becomes left skewed: -10, 1, 2, 3.
Skewed data often occur due to lower or upper bounds on the data. That is, data that have a lower bound are often skewed right while data that have an upper bound are often skewed left.
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