# Generating a boxplot in ArgonStudio

A boxplot (or a box and whisker plot) is a standard way of representing distribution of numerical data using a summary of five numbers:

**the minimum:**the lower bound or the smallest value of the set of numbers.**first quartile (Q**the 25th percentile value or the median of the lower half of the data set._{1}):**median (or Q**the middle value of the data set or the 50th percentile._{2}):**third quartile (Q**the 75th percentile value is the median of the upper half of the data set._{3}):**the maximum:**the upper bound or the largest value in the data set.

## Introduction to boxplots

As explained above, a box plot is a visual representation of
five values which summarize a dataset with
the **minimum**, **first
quartile**, **median**, **third quartile** and
the **maximum**.

Consider the set of the following five numbers.

1, 2, 3, 4, 5

The minimum of the set is `1`, the maximum
is `5`, the median is `3`, Q1
is `2` (in-between the minimum and the median) and Q3
is `4` (in-between the median and the maximum).

Here is how you can generate this boxplot in ArgonStudio.

- Load the ArgonStudio editor.
- Click on the
*Chart*tab at the top. - In the
*Chart data*text box, enter the values as shown in the image above. - In the chart area below the text box, click on
the
*Boxplot*tab. - Choose the X-column and Y-column as shown and click
on
*Draw*.

The boxplot generated shows these values.

## Inter-Quartile Range (IQR) and outliers

The **Inter-quartile range (IQR)** is defined as the
difference between the upper and lower quartiles:

IQR = Q_{3}- Q_{1}

To illustrate outliers, the minimum is defined to be 1.5 times
the IQR below the first quartile or:

min = Q1 - 1.5 * IQR

Similarly the maximum is defined to be 1.5 times
the IQR above the third quartile or:

max = Q3 + 1.5 * IQR

Using these definitions, outliers are defined as those data points that lie outside these limits.

Let us add an outlier to the above data set so that it
becomes:

1, 2, 3, 4, 5, 10

Re-generating the box plot shows the outlier point.

## United States per-capita income by state

Let us now look at some real-world examples of boxplots. The above chart presents per-capita income in the United States for each state when aggregated by the county. The chart shows the box-and-whisker plot of the income as well as the outliers for each state.

## Parts of a boxplot

This image shows the different parts of a boxplot. This image represents the distribution of per-capita income of New York state over each of its counties.

**IQR:**or the inter-quartile range is the difference of the third and the first quartile.**minimum:**this is the lowest value in the dataset (not accounting for the outliers) and is computed as less than Q1 by 1.5 times the IQR.**maximum:**this is the highest value in the dataset (not accounting for the outliers) and is computed as more than Q3 by 1.5 times the IQR.**outliers:**these are the data points which lie outside the range of the distribution.

## Summary

In this article, we covered some basics of boxplots, and how to draw it in ArgonStudio.

- A boxplot shows a representation of the data distribution.
- It includes the dataset
**maximum**and**minimum**at the extremities of the whiskers. - The box represents the
**first quartile (Q**and the_{1})**third quartile (Q**at the box ends, and a line inside the box as the_{3})**second quartile (Q**(also known as the_{2})**median**). - Any
**outliers**are shown as points outside the whiskers.