Statistics Definitions > Pearson Mode Skewness

Pearson mode skewness, also called *Pearson’s first coefficient of skewness*, is a way to figure out the skewness of a distribution.

The mean, mode and median can be used to figure out if you have a positively or negatively skewed distribution.

- If the mean is greater than the mode, the distribution is positively skewed.
- If the mean is less than the mode, the distribution is negatively skewed.
- If the mean is greater than the median, the distribution is positively skewed.
- If the mean is less than the median, the distribution is negatively skewed.

## Pearson Mode skewness

Pearson mode skewness uses the above facts to help you find out if you have positive or negative skewness. If you have a distribution and you know the mean, mode, and standard deviation (σ), then the Pearson mode skewness formula is:

**(mean-mode)/σ **

**Sample problem: **You have data with a mean of 19, a mode of 20 and a standard deviation of 25. What does Pearson Mode Skewness tell you about the distribution?

(mean-mode)/σ = (19-20)/25 = -0.04.

There is a very slight negative skewness (-0.04). **Note**: For most intents and purposes, this would count as a symmetric distribution as the skewness is so small.

## Pearson Mode Skewness: Alternative Formula.

If you don’t know the mode, you won’t be able to use Pearson mode skewness. However, the direction of skewness can be also figured out by finding where the mean and the median are. According to Business Statistics, this leads to a second, equivalent formula:

**3(Mean – Median) / σ**

This formula is also called Pearson’s second coefficient of skewness.

## Pearson Mode Skewness: What the Results mean.

The difference between the mean and mode, or mean and median, will tell you how far the distribution departs from symmetry. A symmetric distribution (for example, the normal distribution) has a skewness of zero.

Both equations give you results in standard deviations, which are dimensionless units of measurement from the mean.

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In my study, Pearson’s skewness value is 0.086. What is the acceptable value for Pearson’s skewness?

I’m not quite sure what you mean by “acceptable”, as skew could technically be any number. As your skew is so small, it’s practically a normal distribution.

In my data set I have a mean that is greater than the mode, and a median greater than the mean. I have a standard deviation of 0.4632 and when I calculated the skew using the first formula, I came out with a skew of 1.6459. How does this relate to the graph diagrams earlier in the page where you described the mean as being the largest, then the median, then the mode?

The diagrams give some rules of thumb to enable you to figure out if your data is +/- skewed. Not all data will fit these nice little graphs :)

Looks like you used the formula as you were not able to determine skewness from the RoT.

With a skew of 1.6459, your dataset is positively skewed.

what if i have more than one mode ?

I would take a close look at your data to see if you could separate it (i.e. if you actually have two samples instead of 1). It also depends on where those modes are. If they are close together, you could take an average of the two and use that. But ultimately, it really depends on what you are trying to do with the data. If you’re trying to compare two distributions to see which is more skewed then the average method should work just fine.

Kkkkkk

Nice..☺☺

This work has provided a greater opportunity for me to learn Statistics.

What you do If you have 3 or more modes ?

Thanks you made life easier for me