> For the complete documentation index, see [llms.txt](https://dshub.gitbook.io/ds-hub/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://dshub.gitbook.io/ds-hub/statistics/fundamentals/central-tendency-asymmetry-and-variability.md).

# Central Tendency, Asymmetry, and Variability

The Central Tendency is measured by 3 parameters:

* Mean: Average
* Median: Mid point
* Mode: The most frequent 

<figure><img src="https://483934582-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F332OmkaCCBc9TZFZXfnO%2Fuploads%2FQWyPpso97Mgf7fpL0SbC%2Fsamplevspopulation-mean.png?alt=media&amp;token=58f27c35-ce97-4ca6-a7ff-7c3e59b0f9a8" alt="" width="369"><figcaption><p>Credit: <a href="https://www.onlinemathlearning.com/population-mean.html">https://www.onlinemathlearning.com/population-mean.html</a></p></figcaption></figure>

The most common method to measure Asymmetry is so called the Skewness. There are 3 types of skewness our data can hold:

* Zero Skew: the data are symmetric and form a bell shape&#x20;
* Negative (Left) Skew: the left-tailed, the outliers are on the left-side
* Positive (Right) Skew: the right-tailed, the outliers are on the right-side

<figure><img src="https://483934582-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F332OmkaCCBc9TZFZXfnO%2Fuploads%2FSW5BlNb2rnloQ2ajx1CM%2Fimg_91a4bcaa0b9b-15331990616072639890.jpg?alt=media&amp;token=9dd03096-2363-4f49-85a9-2b7e03a47b47" alt=""><figcaption><p>Credit: <a href="https://study.com/academy/lesson/skewness-in-statistics-definition-formula-example.html">https://study.com/academy/lesson/skewness-in-statistics-definition-formula-example.html</a></p></figcaption></figure>

The skewness tells us where our data are mostly situated and acts as a bridge between the Central Tendency and Probability Distribution.

{% hint style="info" %}
Note that the skewness may be hard to see especially when we use wide bin sized histograms. Therefore it is best to use the mathematical formula to see how skewed our data set is.
{% endhint %}

The Variability (Dispersion/Spread/Variance) is calculated separately per Sample and Population.

<figure><img src="https://483934582-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F332OmkaCCBc9TZFZXfnO%2Fuploads%2FSwaQeCAm1tJw97tccS6j%2Fsamplevariance.png?alt=media&amp;token=fc96c0e6-129a-4d6f-9536-e523581b4d6f" alt=""><figcaption><p>Sample Variance</p></figcaption></figure>

<figure><img src="https://483934582-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F332OmkaCCBc9TZFZXfnO%2Fuploads%2FkG0uqsukPtnJCBrP17Q8%2Fpopvariance.png?alt=media&amp;token=81395332-6179-4b7b-88ee-a3af10d010fc" alt=""><figcaption><p>Population Variance</p></figcaption></figure>

Why is it Squared?

1. Dispersion is non-negative
2. Non-negative values do not cancel out
3. Amplifies the effect of large differences