Understanding skewness is important not only in statistics but also in real-world applications involving data analysis. This article introduces and demystifies the concept of data skewness, providing visual examples of real-world skewed data, guidelines on how to interpret skewness, and thoughts on whether or not skewness should be deemed a problem in the data.

What is Skewness?

In statistical terms, skewness measures how asymmetric a dataset is around its mean. If data is symmetric, it is not skewed, and vice versa. To better understand the difference between symmetric and skewed data, a picture is worth a thousand words.

Symmetric vs. skewed data | Image by Author

As we can observe, the distribution of symmetric data is rather balanced around its center, where the “peak” around which most frequent instances lie is located. Meanwhile, in skewed data, this peak is shifted towards a side of the distribution, with a “long tail” extending to the other side.

Did you notice in the above plot the term right-skewed distribution? This is one of the two broad types of skewness, occurring when most data points or instances cluster on the left where the peak rises, while a long tail extends to the right, indicating there exist a few outliers i.e. data points whose values are significantly higher than the rest.

The opposite case is known as left-skewed distribution. When data are left-skewed, most instances cluster on the right, forming a peak there, while a long tail extends to the left. This indicates the presence of a few outliers with values significantly lower than the rest, as shown below.

Left-skewed data | Image by Author

Skewed Data in the Real World

Now that we understand what are right-skewed and left-skewed data, what are real-world examples of both types of skewed data?

Four domains where data are often skewed are:

1. Income distribution: this is a common case of right-skewed data distribution, with most people earning below a small number of high-earning outliers.
2. Housing prices: the distribution of house prices in the real estate sector is another typical case where data tend to be right-skewed, especially in urban areas with a predominance of small apartments whose prices are (comparatively) lower than a smaller number of high-end or luxury properties in such urban areas.
3. Retirement age: the age for retirement is generally described by a left-skewed data distribution, where most people retire shortly before 65-70, and only a few outliers retire at younger ages.
4. Wait times in queues: data describing waiting times at queues is another case of left-skewed data in most situations (well, perhaps there are exceptions … do you often find yourself waiting at the airline check-in counter in an airport?). In these contexts, most waiting times tend to be short, with a few cases being significantly longer waits due to exceptional circumstances.

The four real-world situations and their associated skewed data distributions are illustrated below.

Real-world skewed datasets | Image by Author

Why Does Skewness Matter?

Skewness is important in data analysis as it directly affects the mean and median of your data, along with the way the concept of “average” should be interpreted.

• In right-skewed data, the mean is usually higher than the median, while in left-skewed data, the mean tends to be lower.
• Skewed distributions can also undermine the assumptions of some statistical tests, which rely on data symmetry. In fields like economics and public policy, this is a significant issue, as understanding skewed data, such as income distributions, is essential to making informed decisions.

So, is skewness a problem? The short answer is not necessarily. Data skewness is just one out of many statistical properties or phenomena your data may or may not exhibit, but not necessarily something wrong, as long as you are aware of it and the strategies to deal with it in subsequent data analysis tasks like statistical testing. At the end of the day, it will depend on your analysis’ goals. Skewness only poses a challenge if it skews insights or affects tests with strong normality assumptions. To sum up, skewness often reflects real data patterns that cannot be avoided and can be valuable if dealt with correctly. Deciding whether to process and adjust skewness depends on your specific needs.

Wrapping Up

This article has demystified the concept of skewness: a common statistical phenomenon inherent to many real-world datasets. Through domain-specific examples, we have illustrated situations where left-skewed and right-skewed data distributions are commonly found and discussed the significance, interpretation, and implications of having skewed data.