Box Plots

Introduction

• Box plot is an important concept used in Statistics to represent quantities related to a given dataset graphically and helps us to provide conclusions about that dataset.
• Box plots include graphical representation of these five quantities – Median, Maximum Value, Smallest value, First quartile and the Third Quartile.

Box Plots

• Basically Box Plots are graphical representation of the following quantities which describe a dataset’s important features –
• Example-

• Total values are 15 the increasing order of these will be –

• Median – When the elements of the dataset are sorted (in increasing or decreasing order) then the middle element is called the Median.
• Median will be the middle element that is 4, we can also use the following formula to find median –

• Greatest value – The maximum value among of dataset’s elements.
• In the given example the greatest value is 9.
• Smallest value – The smallest value among the elements.
• In the given example the smallest value is 0.
• Quartile (1^st Quartile) – Basically it is first 25% part of the data. The formula to find 1^st quartile is –

• In the given example-

• Quartile (3rd Quartile) – Basically it is first 75% part of the data. The formula to find 3rd quartile is –

• In the given example-

Solved Examples

Solved Example

Draw the box plot for the following dataset –

SOLUTION

Solved Example

Following is a dataset given that is the time taken by 11 students to complete an essay –

(a) Write down the median time taken (b) Find out the upper and lower Quartiles (c) Draw the box plot for the dataset

SOLUTION

a

Median for the dataset is-

b

The upper and Lower Quartiles-

c

Box plot for the given dataset –

Solved Example

Here is the data collected from a company of the experience of their 10 employees –

Draw the box plot for the data –

SOLUTION

1

To draw the box plot for the given dataset containing an even number of elements first we find Median, Quartiles and Minimum and Maximum value –

2

Final Answer-