Difference Between Skewness and Kurtosis
Skewness and Kurtosis are statistical measures used to describe the shape and characteristics of a distribution in statistics. Skewness is a measure of symmetry (or, more specifically, the lack of symmetry in the data set), which can be positive or negative. In contrast, Kurtosis measures the tailedness of a distribution (i.e., it quantifies the extremity of outliers in the distribution). This article will briefly discuss Skewness and Kurtosis and their similarities and differences.
We always look for skewness and kurtosis while analyzing the data or doing Exploratory Data Analysis. Both measures give information about the shape of the distribution, but they capture the different aspects of the data. Skewness measures the degree of asymmetry in the distribution, while kurtosis measures the degree of peakedness or flatness.
This article will describe what skewness and kurtosis are and the differences between them, and later in the article, we will discuss how to calculate skewness and kurtosis using Python.
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So, let’s start the article by giving the difference between skewness and kurtosis.
Table of Content
- Skewness vs Kurtosis: Difference Between Skewness and Kurtosis
- What is Skewness?
- What is Kurtosis?
- Key Difference Between Skewness and Kurtosis
What is the Difference Between Skewness and Kurtosis?
| Parameter | Skewness | Kurtosis |
| Definition | It measures the degree of asymmetry of a distribution. | It measures the degree of peakedness of a distribution. |
| Calculation | It is the third moment of distribution. | It is the fourth moment of distribution. |
| Range of Values | Values range from -infinity to +infinity | Values range from -infinity to +infinity |
| Interpretation of Values | Negative Skewness: Indicates a long tail on the left-hand side. Zero Skewness: Indicates Perfect Symmetry. Positive Skewness: Indicates a long tail on the right side. |
Platykurtic: It indicates a flatter peak than the normal distribution. It is also referred to as Negative Kurtosis. Zero Kurtosis indicates perfect normality. Leptokurtic: It indicates a sharper peak than the normal distribution. It is also referred to as Positive Kurtosis. |
| Impact on Distribution | Skewness can affect the centre of the distribution. Asymmetrical distribution has a larger impact on the mean than the median. | Kurtosis can affect the tail of the distribution. High kurtosis distribution has more extreme values and can lead to larger standard errors. |
| Example Distribution | Income, wealth, and stock returns are often positively skewed. Distribution, like retirement age, can be seen as negatively skewed. | Exam scores, IQ scores, and reaction time are often leptokurtic. Platykurtic distributions include income, height, and weight. |
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What is Skewness?
Skewness defines the shape of the distribution. Usually, we get a lot of asymmetric distributions, and these distributions have unevenly spread data. There are two types of skewness – positive or right-skewed and negative or left-skewed.
Positive skewness is when the distribution takes place so that we get a long tail towards the right side of the graph. This is called a right-skewed graph,
In this distribution, the mean is greater than the median, which is greater than the mode. That is, we get mean > median > mode.
Negative skewness is when the distribution takes place so that we get a long tail towards the left side of the graph. This is called a left-skewed graph.
What is Kurtosis?
Kurtosis is a statistical measure that describes the degree of peakedness or flatness of a distribution. It measures the shape of the distribution, specifically the height and sharpness of the central peak, relative to that of normal distribution. It is the fourth moment of statistics.
The term “Kurtosis” comes from the Greek word “Kurtos”, which means curved.
Kurtosis is useful to identify the potential outliers in a dataset, as distributions with high kurtosis have more extreme values than normal distributions.
There are three types of Kurtosis: Mesokurtic, Leptokurtic, and Platykurtic.
Types of Kurtosis:
Mesokurtic: This is a type of distribution in which there is symmetry. This means that both the extreme ends of the graph are similar. This is the same as the normal distribution.
Leptokurtic: This distribution has a greater kurtosis than the mesokurtic, which has longer tails. This indicates that a more significant percentage of data is present near the tail, which causes the tail to get longer.
Platykurtic: This distribution has lower kurtosis than the mesokurtic. That is, it has shorter tails. This means there is less data in the tail portion, which makes the tail flatter.
Key Differences Between Skewness and Kurtosis
- Skewness measures the degree of asymmetry of the distribution, while Kurtosis measures the degree of peakedness and flatness of a distribution.
- Skewness is the third measure of moments, while kurtosis is the fourth measure of moments.
- The value of both Skewness and Kurtosis ranges from -infinity to +infinity.
- Both zero skewness and zero kurtosis represent perfect symmetry and perfect normality.
- Skewness can affect the center of the distribution, while kurtosis can affect the distribution’s tails.
- Both Skewness and Kurtosis describe the shape of distributions.
Conclusion
This article briefly covered what skewness and kurtosis are, their types, and their differences. Hope you will like the article.
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FAQs
What is Skewness?
Skewness defines the shape of the distribution. Usually, we get a lot of asymmetric distributions, and these distributions have unevenly spread data. There are two types of skewness – positive or right-skewed and negative or left-skewed.
What is Kurtosis?
Kurtosis is a statistical measure that describes the degree of peakedness or flatness of a distribution. It measures the shape of the distribution, specifically the height and sharpness of the central peak, relative to that of normal distribution. It is the fourth moment of statistics.
What are the key differences between skewness and kurtosis?
Skewness measures the degree of asymmetry of the distribution, while Kurtosis measures the degree of peakedness and flatness of a distribution. Skewness is the third measure of moments, while kurtosis is the fourth measure of moments. The value of both Skewness and Kurtosis ranges from -infinity to +infinity. Both zero skewness and zero kurtosis represent perfect symmetry and perfect normality. Skewness can affect the center of the distribution, while kurtosis can affect the distribution's tails. Both Skewness and Kurtosis describe the shape of distributions.
What are the different types of Skewness?
There are two types of skewness – positive or right-skewed and negative or left-skewed.
Positive Skewness is when the distribution takes place so that we get a long tail towards the right side of the graph. This is called a right-skewed graph,
Negative Skewness is when the distribution takes place so that we get a long tail towards the left side of the graph. This is called a left-skewed graph.
What are the different types of Kurtosis?
Mesokurtic: This is a type of distribution in which there is symmetry. This means that both the extreme ends of the graph are similar. This is the same as the normal distribution.
Leptokurtic: This distribution has a greater kurtosis than the mesokurtic, which has longer tails. This indicates that a more significant percentage of data is present near the tail, which causes the tail to get longer.
Platykurtic: This distribution has lower kurtosis than the mesokurtic. That is it has shorter tails. This means there is fewer data in the tail portion, which makes the tail flatter.
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