In this lesson, you will learn how to describe a statistical distribution by considering its center, shape, spread, and outliers.

Describe a Histogram

At this point, you should be familiar with what a histogram displays. In this lesson, we're going to build on those skills by learning the best way to describe a statistical distribution.

While many people know the functions to plot a histogram, few spend the time to learn how to fully, and concisely communicate what it means. 

In this lesson, you will learn how to interpret a distribution using the following five features of a dataset:

- Center
- Spread
- Skew
- Modality
- Outliers

If you're one for mnemonics, maybe this will help:

**C**ream **S**hoes are **S**tylish, **M**odern, and **O**utstanding.

Throughout this lesson, we will use <a href="https://data.cms.gov/summary-statistics-on-use-and-payments/medicare-geographic-comparisons/medicare-geographic-variation-by-national-state-county" target="_blank">data from the United States Health and Human Services Department</a> to compare the cost of the same medical procedure at over 2,000 hospitals across the country.

Introduction

Once you have the center and range of your data, you can begin to describe its shape. The skew of a dataset is a description of the data's symmetry.

A dataset with one prominent peak, and similar tails to the left and right is called symmetric. The median and mean of a symmetric dataset are similar.

![histogram](https://content.codecademy.com/courses/learn-pandas/distribution-types-ii-symmetric.svg)

A histogram with a tail that extends to the right is called a right-skewed dataset. The median of this dataset is less than the mean.

![histogram](https://content.codecademy.com/courses/learn-pandas/distribution-types-ii-skew-right.svg)


A histogram with one prominent peak to the right, and a tail that extends to the left is called a left-skewed dataset. The median of this dataset is greater than the mean.

![histogram](https://content.codecademy.com/courses/learn-pandas/distribution-types-ii-skew-left.svg)


Skew

An outlier is a data point that is far away from the rest of the dataset. Outliers do not have a formal definition, but are easy to determine by looking at histogram. The histogram below shows an example of an outlier. There is one datapoint that is much larger than the rest.

![title](https://content.codecademy.com/courses/statistics/histograms/histograms-ii/outlier.png)

If you see an outlier in your dataset, it's worth reporting and investigating. This data can often indicate an error in your data or an interesting insight.


Outliers

In this lesson, you learned a framework for describing the distribution of a dataset, which includes the following five features:
- Center
- Spread
- Skew
- Modality 
- Outliers

If you're curious, while the dataset in this study showed the average amount charged by hospitals for a given condition, the amount paid is far less. This is often due to nature of the United States healthcare system, where private insurers negotiate down the charges levied by hospitals.

The small histogram on the left side of the plot displays the actual amount of money paid to the hospital.

Review

One of the most common ways to summarize a dataset is to communicate its center. In this lesson, we will use average and median as our measures of centrality. Take the Codecademy lessons on <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/average/exercises/introduction?action=resume_content_item" target="_blank">average</a> and <a href="https://www.codecademy.com/courses/learn-statistics-with-python/lessons/median/exercises/introduction?action=resume_content_item" target="_blank">median</a> if you're interested in how to calculate them by hand or using NumPy functions.

The figure below shows the average and median ages of a dataset of 100 authors. As expected, the average and median values are near the center of the distribution.

![title](https://content.codecademy.com/courses/statistics/histograms/histograms-ii/mean-median.png)

While it's good practice to communicate both the average and median values, the average is generally more common.

Center

Once you've found the center of your data, you can shift to identifying the extremes of your dataset: the minimum and maximum values. These values, taken with the mean and median, begin to indicate the shape of the underlying dataset. Take the histogram below as an example:

![title](https://content.codecademy.com/courses/statistics/histograms/histograms-ii/mean-median.png)

The minimum value of this data is 18, and the maximum value is 76.

You can calculate the range using the following:

```tex
range = max - min
```

The range of this dataset is
 
```tex
range = 76 - 18 = 58
```

    


Spread

The modality describes the number of peaks in a dataset. Thus far, we have only looked at datasets with one distinct peak, known as _unimodal_. This is the most common.

![histogram](https://content.codecademy.com/courses/numpy/distribution_type_i/unimodal_new.svg)

A _bimodal_ dataset has two distinct peaks. 

![histogram](https://content.codecademy.com/courses/numpy/distribution_type_i/bimodal_new.svg)

A _multimodal_ dataset has more than two peaks. The histogram below displays three peaks.

![histogram](https://content.codecademy.com/courses/numpy/distribution_type_i/multimodal_new.svg)

You may also see datasets with no obvious clustering. Datasets such as these are called _uniform distributions_.

![histogram](https://content.codecademy.com/courses/numpy/distribution_type_i/uniform_new.svg)