Box Plots

Box & Whiskers Plot - Definition n Construction

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 that 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.




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.

The box and whisker plot displays how the data is spread out. In the box and whisker diagram, it has five pieces of information,(also called a five-number summary). 

Elements of a Box and Whisker Plot

The elements required to construct a box and whisker plot outliers are given below.

Minimum value (Q0 or 0th percentile)

First quartile (Q1 or 25th percentile)

Median (Q2 or 50th percentile)

Third quartile (Q3 or 75th percentile)

Maximum value (Q4 or 100th percentile)

Interquartile range

The meaning of each of these elements is listed below.

  • The minimum value in the dataset, which is displayed at the far left end of the diagram.
  • The first quartile (Q1) at the left side, which is in between the minimum value and median.
  • The median value, represented by the line in the center of the box.
  • The third quartile (Q3) at the right side, which is in between the median and the maximum value.
  • The maximum value in the dataset, which is displayed at the far right end of the diagram.
  • Interquartile range (IQR) is the difference between upper and lower quartiles, i.e. Q3 and Q1.


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

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.


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