What is a Box and Whisker Plot?
A box and whisker plot is a graphical representation of the collected data on a number line with the use of the least value, greatest value and the quartiles, as explained earlier.
A box and whisker plot shows the variability of a given data set.
From the image we can observe that there are five numbers, that is, least value, first quartile, second quartile(median), third quartile and the greatest value. Therefore the box and whisker plot is also called the five number summary of a data set.
Quartiles divide the the data into four equal parts, the first quartile is the \(25^{th}\) percentile, second is the \(50^{th}\) percentile and the third quartile is the \(75^{th}\) percentile of the data.
How to Draw a Box and Whisker Plot for Data?
These steps will help in drawing a box and whisker plot for any given data:
Step 1: Order the data in an ascending order and find the quartiles.
Step 2: Draw a number line that includes the least value and the greatest value.
Step 3: Graph the points above the number line that represent the five points that represent, the least value, the first quartile, the second quartile(median), the third quartile and the greatest value.
Step 4: Draw the box using the value for the quartiles and draw a line through the median.
Step 5: Draw whiskers from the box to the least and the greatest values.
Shape of Distribution
The shape of distribution of the manner patterns occurring within a given dataset can be seen in a box and whisker plot.
A box and whisker plot shows the shape of distribution as in the table:
Solved Box and Whisker Plot Examples
Example 1: Grade 6 students spent a specific number of hours watching TV. Make a box and whisker plot for this data.
1, 2, 1, 3, 4, 2, 5, 2, 2, 3, 4, 4, 3
Solution:
Step 1: Order the data in ascending order and find the quartiles.
Step 2: Draw a number line that includes the least and greatest values.
Step 3: Graph the points above the number line that represent the five points(least value, first quartile, second quartile or median, third quartile and the greatest value).
Step 4: Draw the box using quartiles and draw a line through the median. Draw whiskers from the box to the least and greatest values.
Example 2: The marks obtained in mathematics out of 20, for eleven students were recorded as 10, 12, 15, 12, 11, 10, 12, 13, 18, 14, 13. Draw a box and whisker plot for the marks.
Solution:
Step 1: Order the data in ascending order and find the quartiles.
Step 2: Draw a number line that includes the least and greatest values.
Step 3: Graph the points above the number line that represent the five points (least value, first quartile, second quartile or median, third quartile and the greatest value).
Step 4: Draw the box using quartiles and draw a line through the median. Draw whiskers from the box to the least and greatest values.
Example 3: A charitable organization came to a school to collect donations. The box and whisker plot in the image represents the donation made from students in grade 6 and grade 7. Identify the shape of distribution of the donation made for both grades.
Solution:
With respect to the donation from the students of grade 7, the left whisker is longer than the right. The median is on the right side of the box. Most data is also on the right.
So, the distribution is skewed left.
With respect to the donations from the students of grade 6, the whisker lengths are equal. The median is in the middle of the box. The left side of the box and whisker plot is a mirror image of the right side of the box and whisker plot.
So, the distribution is symmetric.
A box and whisker plot is also called a five number summary.
The five numbers of a box and whisker plot are least value, first quartile, second quartile (median), third quartile and the greatest value.
A box and whisker plot may be right skewed, symmetric or left skewed.
A box and whisker plot is divided into four parts called,
- first quartile
- second quartile
- third quartile
- fourth quartile