Suppose you wanted to compare three lathes’ performance responsible for the rough turning of a motor shaft. The design specification is 18.85 +/- 0.1 mm.
Diameter measurements from a sample of shafts taken from each roughing lathe are displayed in a box and whisker plot in the figure.
Interpreting a Boxplot
Data science, Machine learning, and many other applicative mathematical fields are all about communicating results, so keep in mind you can always make your boxplots a bit prettier with a little bit of work.
Using the graph, we can compare the range and distribution of the area_mean for malignant and benign diagnosis. We observe that there is a greater variability for malignant tumor area_mean as well as larger outliers.
Also, since the notches in the boxplots do not overlap, you can conclude that with 95% confidence, that the actual medians do differ.
Here are a few other things to keep in mind about boxplots:
- Keep in mind that you can always pull out the data from the boxplot if you want to know what the numerical values are for the different parts of a boxplot.
- The median and the quartiles are calculated directly from the data. In other words, your boxplot may look different depending on the distribution of your data and the size of the sample, e.g., asymmetric and with more or fewer outliers.
A boxplot is a way to show a five-number summary in a chart. The main part of the chart (the “box”) shows where the middle portion of the data is: the interquartile range. At the ends of the box, you” find the first quartile (the 25%
mark) and the third quartile (the 75% mark). The far left of the chart (at the end of the left “whisker”) is the minimum (the smallest number in the set) and the far right is the maximum (the largest number in the set). Finally, the
median is represented by a vertical bar in the center of the box.
Box plots aren’t used that much in real life. However, they can be a useful tool for getting a quick summary of data.
How to Read a Box Plot: Steps
Step 1: Find the minimum.
The minimum is the far left-hand side of the graph, at the tip of the left whisker. For this graph, the left whisker end is at approximately 0.75.
Step 2: Find Q1, the first quartile.
Q1 is represented by the far left-hand side of the box. In this case, about 2.5.
Step 3: Find the median.
The median is represented by the vertical bar. In this boxplot, it can be found at about 6.5.
Step 4: Find Q3, the third quartile.
Q3 is the far right-hand edge of the box, at about 12 in this graph.
Step 5: Find the maximum.
The maximum is the end of the “whiskers”: in this graph, at approximately 16.
Summary
This blog covered the topic of box and whisker plot. A box and whisker plot—also called a box plot—displays the five-number summary of a data set. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
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Frequently Asked Questions
What is data?
Data are characteristics or information, usually numerical, that are collected through observation.
How do you differentiate between data and information?
Data is the raw fact without any add on, but the information is derived from data.
| Data |
Information |
| Raw facts of things |
Data with exact meaning |
| No contextual meaning |
Processed data and organized context |
| Just numbers and text |
|
What are the types of data?
There are two types of Data :
What are the ways to represent data?
Tables, charts, and graphs are all ways of representing data, and they can be used for two general purposes. The first is to support the collection, organization, and analysis of data as part of a scientific study.
What is a box and whisker plot?
A box and whisker plot—also called a box plot—displays the five-number summary of a data set. The five-number summary is the minimum, first quartile, median, third quartile, and maximum.
External References
