# Distributions

Distributions and its properties

Observing the distribution and their characteristics have particular importance in statistics. Distributions describes

- the data
- central tendency behaviour
- dispersion
- identify clusters, peaks and gaps

## Normal Distribution

The normal distribution, also known as the **Gaussian or standard normal distribution**, is the distribution
that all of its values in a symmetrical fashion, and most of the results are situated around the distribution mean.

Normally distribution is perfectly symmetric around its mean. Since the normally distribution is symmetric around
its mean, the measures of central tendency, **Mode, Median** and **Mean** have the following relationship.

mode = median = mean

A normally distributed curve has zero skewness as it is perfectly symmetric around its mean.

#### Normal Distribution Intuition using Python

## Skew Distribution

Skewness is a measure of the asymmetry of the distribution. The skewness value can be positive or negative, or even undefined.

In positively skewed distributions, samples are concentrated towards left of the distribution and has the following central tendency relationship.

mode > median > mean

In negatively skewed distributions, samples are concentrated towards right of the distribution and has the following central tendency relationship.

mode < median < mean

#### Skewed Distribution Intuition using Python

## Co-efficients of Skewness

Skewness can be calculated for a dataset as follows:

Skewness = \( \frac {μ - mode}{σ}\)

Skewness = \( \frac {μ - median}{σ}\)

Skewness = \( \frac {Q1 + Q3 - 2Q2}{Q3 - Q1}\)

If Skewness = 0, the distribution is **symmetric**

If Skewness < 0, the distribution is **negatively skewed or left skewed**

If Skewness > 0, the distribution is **positively skewed or right skewed**

## Share this post

Twitter

Google+

Facebook

Reddit

LinkedIn

StumbleUpon

Pinterest

Email