Left Skewed vs. Right Skewed Distributions

Skewness is a way to describe the symmetry of a distribution.

A distribution is left skewed if it has a “tail” on the left side of the distribution:

 Left skewed distribution

A distribution is right skewed if it has a “tail” on the right side of the distribution:

Right skewed distribution

And a distribution has no skew if it’s symmetrical on both sides:

Distribution with no skew

Note that left skewed distributions are sometimes called “negatively-skewed” distributions and right skewed distributions are sometimes called “positively-skewed” distributions.

Properties of Skewed Distributions

The following diagrams show where the mean, median and mode are typically located in different distributions.

Left Skewed Distribution: Mean < Median < Mode

Mean vs. median vs. mode in left skewed distribution

In a left skewed distribution, the mean is less than the median.

Right Skewed Distribution: Mode < Median < Mean

Mean vs. median vs. mode in right skewed distribution

In a right skewed distribution, the mean is greater than the median.

No Skew: Mean = Median = Mode

Mean vs. median vs. mode in symmetrical distribution

In a symmetrical distribution, the mean, median, and mode are all equal.

Using Box Plots to Visualize Skewness

box plot is a type of plot that displays the five number summary of a dataset, which includes:

  • The minimum value
  • The first quartile (the 25th percentile)
  • The median value
  • The third quartile (the 75th percentile)
  • The maximum value

To make a box plot, we draw a box from the first to the third quartile. Then we draw a vertical line at the median. Lastly, we draw “whiskers” from the quartiles to the minimum and maximum value.

Depending on the location of the median value in the boxplot, we can tell whether or not a distribution is left skewed, right skewed, or symmetrical.

Visualizing skewness with boxplots

When the median is closer to the bottom of the box and the whisker is shorter on the lower end of the box, the distribution is right skewed.

When the median is closer to the top of the box and the whisker is shorter on the upper end of the box, the distribution is left skewed.

When the median is in the middle of the box and the whiskers are roughly equal on each side, the distribution is symmetrical.

Examples of Skewed Distributions

Here are some real-life examples of skewed distributions.

Left-Skewed Distribution: The distribution of age of deaths.

The distribution of the age of deaths in most populations is left-skewed. Most people live to be between 70 and 80 years old, with fewer and fewer living less than this age.

Example of left-skewed distribution

Right-Skewed Distribution: The distribution of household incomes.

The distribution of household incomes in the U.S. is right-skewed, with most households earning between $40k and $80k per year but with a long right tail of households that earn much more.

Example of right skewed distribution

No Skew: The distribution of male heights.

It’s well-known that the height of males is roughly normally distributed and has no skew. For example, the average height of a male in the U.S. is roughly 69.1 inches. The distribution of heights is roughly symmetrical, with some being shorter and some being taller.

Example of distribution with no skew

Additional Resources

5 Examples of Positively Skewed Distributions
5 Examples of Negatively Skewed Distributions
How to Calculate Skewness in Excel
How to Identify Skewness in Box Plots

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6 Replies to “Left Skewed vs. Right Skewed Distributions”

  1. どうもありがとうございます!これは私を大いに助けました!あなたはより多くを作る必要があります!
    Thank you so much! This helped me a lot! You should make more! (Sorry I’m using google translate for my English is bad)

  2. Just came across this fantastic explanation on skewed distributions by Zach! It’s concise and easy to understand, making it perfect for anyone trying to grasp the concept. The visuals and real-life examples really help clarify the topic. Great job, Zach! 🙌

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