# Skewed usage of skewed distribution

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- Skewed usage of skewed distribution

## Skewed usage of skewed distribution

Some time ago, the *CM Define It* app featured the phrase *skewed distribution*. *Skewness* refers to the measure of the extent of asymmetry (wonkiness) of a distribution (usually of data) (Weisstein, n.d.). Different types of skewness exist. A *positive skew* happens when the wonky distribution of data has the “lump” of data occurring at the start, followed by a long “tail” – this is also called a *right-skewed distribution* as the tail is to the right. A distribution that has a *negative skew* occurs when the long tail happens first which is then followed by a lump of data – also called a *left-skewed distribution* as the tail is to the left (MathsIsFun, 2020).

Figure 1. Left-skewed and right-skewed distributions

We decided to take a look at how popular the term *skewed distribution* has been over time using the Google Books Ngram viewer.

Figure 2. Frequency of use of the term skewed distribution over time, as a percentage of words indexed by Google Books

The graph shows an interesting increase in the use of the term skewed distribution in books from the early 1900s. After a slight dip around the 1940s, there is a steep spike in the appearance of the term that continues until the 1980s, which then levels off.

The two questions that spring to mind are:

- Why is there an increase in the frequency of use of the term skewed distribution from 1910?
- Why is there a sharp rise in the frequency of use of the term skewed distribution between 1940 and 1980?

Groeneveld and Meeden (1984) suggest that statistical literature has featured the topic of skewed distributions for a long time. In 1895, the mathematician Karl Pearson talked about the gamma distribution model for skewed data, and in 1897 Vilfredo Pareto, an economist, showed an interest in skewed distributions in the context of economy and income (Pearson, 1895; Pareto, 1897, as cited in Groeneveld & Meeden, 1984). Perhaps interest in skewness at the end of the 1890s contributed to the slight increase in the frequency of the use of the term in books around 1910? As Pearson’s writings became more known, perhaps more books and literature studying skewed distributions appeared?

How can we explain the sharp rise in the frequency of use of the phrase skewed distribution between 1940 and 1980? Doane and Seward (2011) suggest that since Pearson’s famous writings in 1895, many more statisticians have investigated and written about the properties of statistics of skewness. Yule and Kendall’s (1950) 3rd edition of *An Introduction to the Theory of Statistics* and Kenney and Keeping’s (1954) 3rd edition of *Mathematics of Statistics* – both prominent writings – were published in the 1950s, shortly after the increase in the frequency of the phrase skewed distribution starts. Additionally, Kenney’s 2nd edition of *Mathematics of Statistics* was published in 1947 – around the time when the spike starts.

Do you think that the importance of the above writings contributed to the increase in the appearance of the term skewed distribution in books? Can you explain the above trends differently? Do you have other suggestions? If so, get in touch with us by commenting below or by emailing us.

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**References:**

Doane, D. P., & Seward, L. E. (2011). Measuring skewness: A forgotten statistic? *Journal of Statistics Education, 19*(2), 1-18. http://jse.amstat.org/v19n2/doane.pdf

Groeneveld, R. A., & Meeden, G. (1984). Measuring skewness and kurtosis. *Journal of the Royal Statistical Society. Series D (The Statistician), 33*(4), 391-399. https://www.jstor.org/stable/2987742

Kenney, J. F. (1947). *Mathematics of statistics: Part one* (2nd ed.). D. Van Nostrand and Company, Inc.

Kenney, J. F., & Keeping, E. S. (1954). *Mathematics of statistics: Part one* (3rd ed.). D. Van Nostrand and Company, Inc.

MathsIsFun. (2020). *Skewed data*. Maths Is Fun. https://www.mathsisfun.com/data/skewness.html

Weisstein, E. W. (n.d.). *Skewness*. Wolfram MathWorld. https://mathworld.wolfram.com/Skewness.html

Yule, G. U., & Kendall, M. G. (1950). *An introduction to the theory of statistics* (3rd ed.). Harper Publishing Company.

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