# Distribution

- What is
**Normal Distribution?** - What is
**Margin of Error?** - What is
**Skewness?** - What is
**Kurtosis?**

## Normal Distribution

The **Normal Distribution Curve** is a bell-shaped curve.

Each band of the curve has a width of **1 Standard Deviation**:

Each band of the curve has a width of 1 Standard deviation from the **Mean Value**.

Values less than **1 Standard Deviation**
away account for **68.27%**.

Values less than **2 standard deviations** away account for **95.45%**.

Values less than **3 standard deviations** away account for **99.73%**.

What does it mean?

Most observations are within 1 standard deviation from the mean.

Almost all observations are within 2 standard deviations.

Practically all observations are within 3 standard deviations.

## Normal Distribution Facts

Normal distribution is **Symmetric**. The peak always divides the distribution in half.

Normal distribution is a **Probability** distribution.

A lot of observations follow the normal distribution:

- Your IQ
- Your Weight
- Your Height
- Your Salary
- Your Blood Pressure

Normal distribution shows that values near the mean are more frequent than values far from the mean:

Distance from the Mean Value | Percentage of the Population |
---|---|

1 Standard deviation | 68.27% |

2 Standard deviations | 95.45% |

3 Standard deviations | 99.73% |

The **68–95–99.7 Rule** (aka The Empirical Rule), is a shorthand
to remember the percentage of values that lie within the different bands of a normal distribution.

Normal distribution is also known as the **Gaussian Distribution** and the **Bell Curve**.

## The Margin of Error

Statisticians will always try to predict everything with 100% accuracy.

But, there will always be some uncertainty.

The** Margin of Error** is the number that quantifies this statistical uncertainty.

**Different margins** define different ranges for where we believe the correct answers can be found.

**The acceptable margin** is a matter of judgment, and relative to how important the answer is.

The more samples we collect, the lower the margin of error is:

## How to Interpret Margin of Error

Suppose 55% of a sampled population say they plan to vote "Yes".

When projecting this to a whole population, you add/subtract the margin of error to give a range of possible results.

With a margin of error of 3%, you are confident that between 52% and 58% will vote "Yes".

With a margin of error of 10%, you are confident that between 45% and 65% will vote "Yes".

## Skewness

**Skewness** is a distortion (an asymmetry) from the bell curve (normal distribution).

## Kurtosis

**Kurtosis** is a also a distortion from the normal distribution (bell curve).

While skewness describes a unexpected values in one tail, kurtosis describes unexpected values in both tails.

Image: Negative kurtosis (lower than normal distribution).

Image: Positive kurtosis (higher than normal distribution).