TRATON STATISTICS: Math Lesson for the Day - Simple Calculations of Skewness

Various organizations gather information for purposes of statistical analysis. Oftentimes, reporting the raw numbers results in an unmanageable (and often difficult-to-decipher) mess. Consequently, instead of reporting all of the raw numbers, these organizations report the data size (n), quartiles (Q1, Q3), medians (m), means (M), etc. Sometimes, to the misfortune of the inquisitive reader, these reporting organizations only report some of the statistical information (e.g., Q1, Q3, m), thereby leaving the reader to calculate other statistical information. Additionally, while the data-gathering organizations frequently presume that the data is normally distributed, this is often not true, and the distribution exhibits some type of skew.

Through this article, we provide a simple way of calculating some of the useful information associated with a statistical distribution when only a limited amount of information is provided. Specifically, this article explains a simple way to calculate:

(a) skewness (S),

when one knows the:

(a) median (m);
(b) mean (M);
(c) first quartile (Q1, which is 25%); and
(d) third quartile (Q3, which is 75%).

The simplified equation for skewness (S) is:

Eq. 1
S = 3(M-m)/SD

where:

Eq. 2
SD = 0.7413(Q3-Q1)

In our next article, my colleague Ingrid Ingram will discuss the calculations of particular quantiles in view of other known statistical information.

Reporting for Traton News,

Morley Moore.