What is Skewness & Kurtosis ?

What is Skewness & Kurtosis ?

Understanding Skewness and Kurtosis in Statistics

When analyzing data, we often encounter distributions that deviate from the idealized bell-shaped curve. Skewness and kurtosis are two statistical measures that help us understand the shape and characteristics of these distributions.

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Skewness:

Skewness refers to the asymmetry of a distribution. Imagine a histogram representing data points. In a perfectly symmetric distribution (like a normal distribution), the left and right tails are equal in length. However, real-world data often exhibit skewness.

  • Positive skewness: The tail extends more to the right (higher values). For example, income distributions often have positive skewness because a few high earners pull the average upward.
  • Negative skewness: The tail extends more to the left (lower values). An example is the distribution of exam scores, where a few students perform poorly and drag the average down.

Skewness helps us understand the concentration of data around the mean. A symmetric distribution has zero skewness.

Kurtosis:

Kurtosis measures the “peakedness” or “flatness” of a distribution. Here’s what you need to know:

  • A normal distribution (like the bell curve) has moderate kurtosis.
  • High kurtosis: The curve is more peaked, resembling a sharp mountain peak. This occurs when data points cluster closely around the mean.
  • Low kurtosis: The curve is flatter, resembling a plateau. It indicates a broader spread of data.

Why does kurtosis matter? It informs our choice of statistical techniques. For instance, high kurtosis may require robust statistical methods.


In summary, skewness and kurtosis provide valuable insights into the shape of data distributions. As data analysts, understanding these concepts helps us make informed decisions and choose appropriate models.


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Prabhakar G

Six Sigma Black Belt, Advance Problem Solving, Deming Daily Mgmt, Manufacturing Quality, Vendor Quality, TQBM, QMS, Gemba DD, Plant Capital Budgeting & Projects, Guide and Mentor the Advance Problem Solving projects.

4 个月

Simple and clear explanation

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very informative

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Luis Mata

Quality Systems Manager

4 个月

Your Control Charts have information, all that you need to do is how you will manage your information. If you can dive deep in your data for a proper analysis

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Kurtosis does NOT measure peakedness or flatness. You can have infinitely peaked distributions with very low kurtosis, and you can have perfectly flat-topped distributions with very high kurtosis. Kurtosis measures tail weight.

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Bob James

President at Thermaflo Incorporated

4 个月

We have employed this in many areas of our manufacturing process

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