## Comparing Distributions

## Overview

When you compare two or more distributions you want to look at the shape, center, spread, and unusual features. It is the same criteria when describing a distribution as comparing distributions.

Image from: http://andrewpwheeler.files.wordpress.com/2012/04/uneven_dist1.png

Image from: http://andrewpwheeler.files.wordpress.com/2012/04/uneven_dist1.png

## Comparing Multiple Distributions

The most common way to compare three or more distributions is with boxplots. Things to look at are the medians, interquartile ranges, and outliers.

image from: http://www.fda.gov/ucm/groups/fdagov-public/documents/image/ucm127531.gif

image from: http://www.fda.gov/ucm/groups/fdagov-public/documents/image/ucm127531.gif

## Final Reminder

__Shape__: described by the symmetry, skewness, number of peaks.__Center__: the median__Spread__: the variability or range__Unusual features__: gaps and outliers

**Example 1:**

Compare the distributions.

*Answer:*

shape – both are roughly symmetric and are unimodal.

center – the median amount of boys is 42 and the median amount of girls is 36.

spread – the amount of boys is from 7 to 73 with a range of 66 and the amount of girls is 11 to 54 with a range of 43. The amount of boys is more vaired than the girls.

unusal features – no outliers or gaps.

shape – both are roughly symmetric and are unimodal.

center – the median amount of boys is 42 and the median amount of girls is 36.

spread – the amount of boys is from 7 to 73 with a range of 66 and the amount of girls is 11 to 54 with a range of 43. The amount of boys is more vaired than the girls.

unusal features – no outliers or gaps.

**Example 2:**

Compare the distributions

*Answer:*

shape – both are unimodal. Block B is slightly right skewed.

center – the median of Block A is 1 and the median of Block B is 2.

spread – Block A’s range is from 0 to 4 and the range of Block B is from 0 to 6.

unusual features – no gaps or outliers

shape – both are unimodal. Block B is slightly right skewed.

center – the median of Block A is 1 and the median of Block B is 2.

spread – Block A’s range is from 0 to 4 and the range of Block B is from 0 to 6.

unusual features – no gaps or outliers