#boxplots

Last week, I posted about implementing design principles in Python's graphic library, matplotlib. I received lots of great feedback, and made another tutorial, specifically about boxplots and "small multiples". Small multiples are a concept coined by Edward Tufte about having many plots using the exact same axes, allowing the reader to discover patterns by eye, though here I also add linear regression to aid the eye.

In mathematics we graphed our numerical data in many ways. By graphing the data we can easily understand the solution of the problem. For this we have so many types of graphs like bar charts, histogram and many more. Box plots are one of them. It is also known as a box and whisker diagram. Box plots in statistics are the appropriate way by which we can represent the group of numerical data in a graphical manner through their five number summaries.

Now the question arises is; what are the five number summaries, so the answer is:

1.     Minimum

2.     Maximum

3.     Lower quartile

4.     upper quartile

5.     Median

All the above are the measures of distribution that gives the whole descriptions about the series. We can make box plots either horizontally or vertically. Box plots are useful to display the difference between populations. Box plots are useful to measure the shape, middle value and variability. Although box plots do not gives the detail descriptions like histogram and stem and leaf graph gives. Box plots are useful when we have large numbers of values in a given set.

To draw the box plot first we have to arranger the numbers in an order than we find the maximum, minimum and quartiles. The first value and last value will be the minimum and maximum respectively. To find maximum, minimum and quartiles we have formulas.

For first quartile that is lower quartile Q1 = (n + 1th) item / 4

For second quartile that is median Q1 = (n + 1th) item / 2

For third quartile that is upper quartile Q3 = 3(n + 1th) item / 4