All About Whisker and Box Plot

Whisker boxplot serves some sort of the same purpose as the standard deviation, but more visually. It lets us know the overall behavior or dispersion of the data without having to look into the dataset closely.

For understanding whisker boxplot, we need to be familiar with an important term widely used in statistics, that is 5-number-summary of a dataset. The 5 numbers include the minimum value, Quartiles (all 3 of them) and the Maximum value. I will explain all of them in the easiest way possible and lead you comfortably to our today’s agenda- Whisker boxplot.

Maximum and Minimum value: Just the largest and the smallest value/data within a dataset.

Quartiles: Quartiles have only three parts- Q1, Q2, Q3. Please note that Quarters and Quartiles are different things. Unlike Quarters, Quartiles have no Q4. However, Quartiles divide the data into four regions.

To plot a Whisker boxplot manually, finding all the quartiles is a must. Finding the quartiles are very easy. Q2 is simply the median value of a dataset. I will demonstrate the whole process.

Finding quartiles for an ODD number of data within a dataset:

`Data: 8,9,2,10,3,5,7,12,15Order: 2,3,5,7,8,9,10,12,15So, Median 8 (Middle one). This is Q2. `
`Q1 is the median that comes from the lower half of the data.Now the lower half: 2,3,5,7,8So, Q1 is 5.`
`Q3 is the median that comes from the upper half of the data.Now, the upper half: 8,9,10,12,15So, Q3 is 10.`

Finding quartiles for an EVEN number of data within a dataset:

`Data: 10,12,14,15,14,16,17,18,10,19,17,17Order: 10,10,12,14,14,15,16,17,17,17,18,19`
`As the number of data is Even, so to find the median, we have to find the average of the middle two data.Average of 15 and 16 is 15.5. So, Median is 15.5. This is Q2. `
`Q1 is the median that comes from the lower half of the data.Now the lower half: 10,10,12,14,14,15Average of 12 and 14 is 13. So, Q1 is 13.`
`Q3 is the median that comes from the upper half of the data.Now, the upper half: 16,17,17,17,18,1Average of 17 and 17 is 17.So, Q3 is 17.`

Now that we all understand 5-number-summary of data, let's go with a real-world challenge that can be easily solved and visualized with whisker boxplot using our 5-number-summary theory.

Example scenario:

Professor Jarvis took an exam on two sections (let us name them Section A and Section B) under his department with the exact same question paper. He wanted to determine which section does better in the exam than the other one. He is pretty wise, like us, wanted to visualize the performance through a whisker boxplot. Therefore, he has collected the 5-number-summary of both classes for that exam; the maximum, the quartiles and the minimum score in each class.