Box Plot

plots r

Box Plot

This is a Plot that can be useful for Exploratory Data Analysis
This plot is a visualization of Summary Statistics
it’s “a convenient way of graphically depicting groups of numerical data through their quartiles”

General idea:

What is Distribution of data?
- is it compact? symmetric?
Are there Outliers?

IQR = Q3 - Q1 - the length of the box
whiskers (fences) capture data outside of the box

```text only boxplot(…, range=0, …) boxplot(…, horizontal=T, …) // horizontal boxplot

<code>range=0</code> means that it will show usual box plot.


### Modified Box Plot
''Modified box plot'' can be used to show [Outliers](Outliers)

- IQR (''Inter Quartile Range'') - difference between 3rd and 1st quartile 
- ''Inner fences'' - the values that are 1.5 times the IQR beyond the 1st and 3rd quartile 
- Lower inner fence = 1st quartile - (1.5 x IQR)
- Upper inner fence = 3rd quartile + (1.5 x IQR)
- observations beyond the whiskers (fences) are outliers and marked with dots 


<img src="https://raw.githubusercontent.com/alexeygrigorev/wiki-figures/master/crs/da/boxplot-modified.png" alt="Image">

In R
- by default <code>boxplot</code> shows modified box plot
- <code>IQR(data)</code> shows the IQR


## [Bivariate Analysis](Bivariate_Analysis)
We can calculate [all 5 number](Summary_Statistics) values for all quantitative variables associated with a specific category.
- And for each category get a box plot 
- With box plots, we also can see how two values interact 
- <img src="https://raw.githubusercontent.com/alexeygrigorev/wiki-figures/master/crs/da/boxplot-bivariate.png" alt="Image">


### R
```text only
boxplot(d$a ~ as.factor(d$f))

it will show separate boxplot of values in $a$ for each values of $f$

boxplot(d$a ~ as.factor(d$f), col=c("blue","orange"), names=c("yes","no"), varwidth=T)

if we want to show how much data is there for each factor,
we can make the with of the boxes proportional to the volume of data
using varwidth=T

Box Plot with Other Plots

Box plots are nice to combine with other plots

for example, with a Scatter Plot
[http://www.statmethods.net/advgraphs/layout.html]
This is the R snipped to produce this figure

Sources

Statistics: Making Sense of Data (coursera)
Data Analysis (coursera)
http://en.wikipedia.org/wiki/Box_plot

✏️ Edit on GitHub

Box Plot

Box Plot

Box Plot with Other Plots

See Also

Sources