The **normal distribution** is essential when it comes to statistics. Not only does it approximate a wide variety of variables, but decisions based on its insights have a great track record.

If this is your first time hearing the term ‘**distribution**’, don’t worry. We have an article where we explain that the **distribution** of a dataset shows us the frequency at which possible values occur within an interval. There, we also mention several other fundamental distributions.

Experienced statisticians can immediately distinguish a **Binomial** from a **Poisson** **distribution**.

They can also tell if a certain **distribution** is either **Uniform** or **Exponential** with a quick glimpse at a plot.

**Which Distributions We Will Focus on**

In our tutorials, we will focus on the **normal** and **student’s T** **distributions.**

These are the reasons why:

- They approximate a wide variety of random variables.
**Distributions**of sample means with large enough sample sizes could be approximated to normal.- All computable statistics are elegant.
- Decisions based on
**normal distribution**insights have a good track record.

If it sounds like gibberish now, we promise that after a few paragraphs, you will understand it.

**Visualizing a Normal Distribution**

In the picture below, you can see a visual representation of a **Normal distribution**.

You have surely seen a **normal distribution** before because it is the most common one. The statistical term for it is **Gaussian distribution**. Though, many people call it the **Bell Curve,** as it is shaped like a bell.

It is symmetrical and its **mean**, **median** and **mode** are equal.

If you know what **skewness** is, you will recognize that it has no skew! It is perfectly centred around its **mean**.

**How it’s Denoted**

**N** stands for normal and the tilde sign(~) shows it is a **distribution.** In brackets, we have the **mean(μ)** and the** variance(σ ^{2})** of the

**distribution**

On the plane, you can notice that the highest point is located at the **mean**. This is because it coincides with the **mode**. The spread of the graph is determined by the **standard deviation**, as it is shown below.

**Understanding the Normal Distribution**

Below, you can see an approximately normally distributed **histogram**.

There is a concentration of the observations around the **mean**. This makes sense because it is equal to the **mode**.

Moreover, it is symmetrical on both sides of the **mean**.

We used 80 observations to create this **histogram**. As shown below, its **mean** is 743 and its **standard deviation** is 140.

But what if the **mean** is smaller or bigger? Let’s first zoom out a bit by adding the **origin** of the graph. The **origin** is the zero point. As you can tell from the picture below, adding it to any graph gives perspective.

**Controlling for the Standard Deviation**

Keeping the **standard deviation** fixed, a lower **mean** would result in the same shape of the **distribution**, but on the left side of the plane. This is called controlling for the **standard deviation**.

In the same way, a bigger **mean** would move the graph to the right, as shown in the picture below.

In our example, this resulted in two new **distributions.** One is with a **mean** of 470 and a **standard deviation** of 140. Whereas the other one is with a **mean** of 960 and a **standard deviation** of 140.

**Controlling for the Mean**

Now, let’s do the opposite.

Controlling for the **mean**, we can change the **standard deviation** and see what happens. From the picture below, you can tell that this time the graph is not moving. But it is rather reshaping.

A lower **standard deviation** results in a lower dispersion, so more data in the middle and *thinner tails*.

On the other hand, a higher **standard deviation** will cause the graph to flatten out with fewer points in the middle and more to the end. Or in statistics jargon – *fatter tails*.

**What’s Next**

These are the basics of a **normal distribution**. You can recognize it by looking at its **mean**, **median** and **mode**. If they are equal and it has no **skew**, it is indeed normal. After reading this tutorial, you should be able to control for the **standard deviation** and for the **mean** as well. With this knowledge, you are ready to dive into the concept of **standardization**. In the linked article, you will find out how to create a **standard normal distribution**.

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**Next Tutorial: **Explaining Standardization Step-By-Step