# Is it meaningfull using boxplots for representing the distribution of just four data points?

I'm using boxplots for representing the distribution of some datasets. In one of these datasets I have just four data points. Is it meaningful using boxplots for representing the distribution of such a small sample?

This answer really depends on what you are trying to show in your visualization. As far as quartiles, it won't tell you much; however, say you are looking specifically to show/visualize the range of the data - in this case - it could be a useful tool.

Its meaningful, but that's not important right now. You should ask yourself is it useful? A visualisation should be the answer to a question - what's the question? Does a boxplot of four points answer the question?

Two of these categories are only four points. Can you tell which? Probably not - it doesn't answer the question "How many points?": It does answer "What are the min and max of each category?" and it might also answer "Are any of these data not uniform(0,1)?" because category B looks a bit skewed towards 0 - but you can't really answer that question without knowing the number of points behind the data anyway...

Boxplots are crude tools and so can only answer crude questions.

Okay, here's the count:

> table(d\$Class)

A   B   C   D   E   F
4 100  20   4  20  40


A boxplot is a visualization tool that can help to understand the characteristics of your data. However, the effectiveness of a boxplot depends on the particular dataset being analyzed. In some cases, a boxplot may make the characteristics of the data more evident, while in other cases, it may obscure them. Therefore, there may be alternative visualization techniques that are more appropriate for certain types of data.

In that specific case, a boxplot provides slightly more information than a scatter plot, specifically in regards to the relationship between the highest values in the dataset and Q3. The top whisker indicates how far the maximum value is from Q3 and can identify outliers if it extends beyond Q3+1.5 IQR.

Conversely, a boxplot is not as good as a scatter plot as it does not provide information on the count of cases. The absence of a lower whisker may indicate a concentration of points in Q1, but this is not always the case. To address this limitation, one can superimpose the dots over the boxplot.:

How to plot boxplots superimposed with sorted points using ggplot2. You could also add some jitter and transparency to make a graph better.