# 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):

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

** **** **

**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 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**

## Learning statistics

- Spcforexce.com: Are skewness and kurtosis useful in statistics?

#### Carsten Grube

Freelance Data Analyst

##### Normal distribution

##### Confidence intervals

##### Simple linear regression, fundamentals

##### Two-sample inference

##### ANOVA & the F-distribution

+34 616 71 29 85

Call me

Spain: Ctra. 404, km 2, 29100 Coín, Malaga

...........

Denmark: c/o Musvitvej 4, 3660 Stenløse

**Drop me a line**

*What are you working on just now? Can I help you, and can you help me? *

**About me**

Learning statistics. Doing statistics. Freelance since 2005. Dane. Living in Spain. With my Spanish wife and two children.

**Connect with me**

**What they say**

20 years in sales, analysis, journalism and startups. See what my customers and partners say about me.

## 0 Comments