Bowley skewness is a way to figure out if you have a positively-skewed or negatively skewed distribution. One of the most popular ways to find skewness is the Pearson Mode Skewness formula. However, in order to use it you must know the mean, mode (or median) and standard deviation for your data. Sometimes you might not have that information; Instead you might have information about your quartiles. If that’s the case, you can use Bowley Skewness as an alternative to find out more about the asymmetry of your distribution. It’s very useful if you have extreme data values (outliers)or if you have an open-ended distribution.
Step 1: Find the Quartiles for the data set. You’ll want to look for the “nth” observation using the following formulas:
Q1 = (total cum freq + 1 / 4)th observation = (230 + 1 / 4 ) = 57.75
Q2 = (total cum freq + 1 / 2)th observation = (230 + 1 / 2 ) = 115.5
Q3 = 3 (total cum freq + 1 / 4)th observation = 3(230 + 1 / 4) = 173.25
Step 2: Look in your table to find the nth observations you calculated in Step 1:
Q1 = 57.75th observation = 0
Q2 = 115.5th observation = 1
Q3 = 173.25th observation = 3
Step 3: Plug the above values into the formula:
Skq = Q3 + Q1 – 2Q2 / Q3 – Q1
Skq = 3 + 0 – 2 / 3 – 0 = 1/3
Skq = + 1/3, so the distribution is positively skewed.
In a symmetric distribution, like the normal distribution, the first (Q1) and third (Q3) quartiles are at equal distances from the mean (Q2). In other words, (Q3-Q2) and (Q2-Q1) will be equal. If you have a skewed distribution then there will be a difference between those two values.
Bowley Skewness is an absolute measure of skewness. In other words, it’s going to give you a result in the units that your distribution is in. That’s compared to the Pearson Mode Skewness, which gives you results in a dimensionless unit — the standard deviation. This means that you cannot compare the skewness of different distributions with different units using Bowley Skewness.
- It is an alternative approach to finding skewness when the mean, mode, and standard deviation are not available, but quartiles are known.
- The formula for Bowley skewness is Skq = (Q3 + Q1 - 2Q2) / (Q3 - Q1), where Q1, Q2, and Q3 are the first quartile, second quartile (median), and third quartile, respectively.
- In a symmetric distribution, the first and third quartiles are equidistant from the median. However, in a skewed distribution, there will be a difference between these values.
- Bowley skewness provides an absolute measure of skewness, meaning the result is in the same units as the distribution. This differs from the Pearson Mode Skewness, which is dimensionless.
- It is important to note that Bowley skewness cannot be used to compare the skewness of distributions with different units.
(Note: The information above is based on the concept of Bowley skewness and does not refer to any specific text or passage.)
According to Business Statistics, Bowley recognized that the Bowley Skewness formula could not be used to compare different distributions with different units. For example, you can’t compare a distribution measured in heights in cm with one of weights in pounds. He offered an alternative formula. You should use this formula if you want to compare different distributions with different units:
Relative Skewness = (Q3 + Q1) – (2 * Median / Q3 – Q1).
If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.
|1. What is Bowley's Coefficient of Skewness?|
|2. How is Bowley's Coefficient of Skewness useful in business and statistics?|
|3. How does Bowley's Coefficient of Skewness differ from other measures of skewness?|
|4. What are some limitations of using Bowley's Coefficient of Skewness?|
|5. What are some real-life applications of Bowley's Coefficient of Skewness?|