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Skewness and kurtosis

Even well-defined mean and variance will not tell the whole story of spreads in the probability distribution. Skewness and kurtosis illustrate this when our data is graphed.

 

 

Start by visualizing data

In statistical analysis data we often intent to visualize data as soon as possible. The visualization gives an immediate idea of the distribution of data. We can visualize if data is skewed and if so, if to the left or right and how large the spread is from the mean.

 

 Skewness

Skewness is the degree of distortion from the symmetrical normal distribution bell curve. It compares the extreme values of the tails to each other. Is left tail larger than right tail and vice versa? There are two types of skewness: Right (positive) and left (negative):

 

Skewness and kurtosis

 

As opposed to the symmetrical normal distribution bell-curve, the skewed curves do not have mode and median joint with the mean:

  

Skewness kurtosis

 

Limits for skewness

For different limits of the two concepts, they are assigned different categories. For example, skewness is generally qualified as:

  • Fairly symmetrical when skewed from -0.5 to 0.5
  • Moderately skewed when skewed from -1 to -0.5 (left) or from 0.5 to 1 (right)
  • Highly skewed when skewed from -1 (left) or greater than 1 (right)

 

Kurtosis

How much do the tails differ from the symmetrical bell curve? Is it peaked and are the tails heavy or light? Kurtosis answers for this.

Kurtosis is descriptive or summary statistics and describes “peakedness” and frequency of extreme values in a distribution. Whereas skewness measures symmetry in a distribution, kurtosis measures the “heaviness” of the tails or the “peakedness”.

Kurtosis is useful in statistics for making inferences, for example, as to financial risks in an investment: The greater the kurtosis, the higher the probability of getting extreme values.

So, the further the tails are from the mean the higher the risk of getting an extremely low return and the higher the chance of getting an extremely high return.

The degrees of kurtosis are labeled with leptokurtic, mesokurtic, platykurtic:

 

Skewness and kurtosis

 

 

Skewness and kurtosis in MS Excel

The Excel functions =SKEW and =KURT calculate skewness and kurtosis for a dataset. You can also use Data >> Data Analysis >> Descriptive statistics

Skewness and kurtosis in Excel

 

 

Learning statistics

Carsten Grube

Carsten Grube

Freelance Data Analyst

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