Exploratory Data Analysis: The 5-Number Summary – Two Different Methods in R

Introduction

Continuing my recent series on exploratory data analysis (EDA), today’s post focuses on 5-number summaries, which were previously mentioned in the post on descriptive statistics in this series.  I will define and calculate the 5-number summary in 2 different ways that are commonly used in R.  (It turns out that different methods arise from the lack of universal agreement among statisticians on how to calculate quantiles.)  I will show that the fivenum() function uses a simpler and more interpretable method to calculate the 5-number summary than the summary() function.  This post expands on a recent comment that I made to correct an error in the post on box plots.

> y = seq(1, 11, by = 2)
> y
[1]  1  3  5  7  9 11
> fivenum(y)
[1]  1  3  6  9 11
> summary(y)
     Min.   1st Qu.   Median    Mean     3rd Qu.    Max. 
     1.0     3.5       6.0       6.0      8.5       11.0

Why do these 2 methods of calculating the 5–number summary in R give different results?  Read the rest of this post to find out the answer!

Previous posts in this series on EDA include

• Descriptive statistics
• Box plots
• The conceptual foundations of kernel density estimation
• How to construct kernel density plots and rug plots in R
• Violin plots
• The conceptual foundations of empirical cumulative distribution functions (CDFs)
• 2 ways of plotting empirical CDFs in R
• Conceptual foundations of histograms and how to plot them in R
• Combining histograms and density plots in R