 # Box and Whisker Plot

The process to abstract a set of data which is estimated using an interval scale is called a box and whisker plot. It is also called just a box plot. These are mostly used for data interpretation. We use these box plots or graphical representation to know:

• Distribution Shape
• Central Value
• Variability

When we plot a graph for the box plot, we outline a box from the first quartile to the third quartile. A vertical line which goes through the box is the median. The whiskers (small lines) go from each quartile towards the minimum or maximum value, as shown in the figure below. ## Box and Whisker Plot Definition

A box and whisker plot is a graph that exhibits data from a five-number summary, including one of the measures of central tendency. It does not display the distribution as accurately as a stem and leaf plot or histogram does. But, it is principally used to show whether a distribution is skewed or not and if there are potential unusual observations present in the data set, which are also called outliers. Boxplots are also very useful when huge numbers of data collections are involved or compared.

Since the centre, spread and overall range are instantly apparent, using these boxplots the arrangements can be matched easily.

A box and whisker plot is a way of compiling a set of data outlined on an interval scale. It is also utilised for descriptive data interpretation.

## Box and Whisker Plot Solved Example

Example: Draw the box plot for the given set of data: {3, 7, 8, 5, 12, 14, 21, 13, 18}.

Solution:

Firstly, write the given data in increasing order.

3, 5, 7, 8, 12, 13, 14, 18, 21

Range = Maximum value – Minimum value

Range = 21 – 3 = 18

Now, Median = center value of the given data

Median = 12

Now, we need to find the quartiles.

First quartile = Q1 = Median of data values present at the left side of Median

Q1 = Median of (3, 5, 7, 8)

Q1 = (5+7)/2 = 12/2 = 6

Third quartile = Q3 = Median of data values present at the right side of Median

Q3 = Median of (13, 14, 18, 21)

Q3 = (14+18)/2 = 32/2 = 16

Therefore, the interquartile range = Q3 – Q1 = 16 – 6 = 10

The five-number summary is given by:

Minimum, Q1, Median, Q3, Maximum

Hence, 3, 6, 12, 16, 21 is the five-number summary for the given data.

Now, we can draw the box and whisker plot, based on the five-number summary. ## Box and Whisker Plot Problems

Solve these problems to understand the concept of box plot.

1. Draw a box plot for the given set of data {3, 7, 8, 5, 12, 14, 21, 15, 18, 14}.
2. Find the five-number summary for the given set of data {25,28,29,29,30,34,35,35,37,38}.