Modified Box Plots

Introduction to box plots:

In statistics a box plot can be defined as a diagram explains the summary of data sets. For easy understanding the plots are modified in such a manner that a common man can examine the box plots. Generally creation of box plots involves in finding out the parameters such as median, quartiles, greatest and least observations.

Modified box plots explains the step by step procedure for creating box plots and with the help of it we can evaluate where the observations are concentrated and where they are spread out. As modified box plots are simple to understand they are widely used by many persons in different profession.

Examining Box Plots

Examining box plots is nothing but a process of reading the elements of the plot.

Actually, there are several parameters are available. Namely,

Median
Quartiles
Minimum and maximum values


The following figure shows a typical modified box plots.

Modified box plots



Median:

The median is the value that divides a data set into two parts and it is denoted as Q2.

Quartiles:

As said earlier the median divides the data set into two parts, the first part is known as Lower quartile and later is called as upper quartile.

These quartiles are considered as separate data sets and the median is evaluated.

Lower median is denoted as Q1 whereas upper median is denoted as Q3.

Maximum & Minimum values:

The greatest and the least values of the data set are called as maximum and minimum values respectively.

Outliers:

Upper outlier is the value which is more than 3/2 times of upper quartile and Lower quartile is the value which is less than 3/2 times of lower quartile.Is this topic Greatest Common Factor Word Problems hard for you? Watch out for my coming posts.

Example

Consider the following data set.

Data set => (12, 4, 9, 66, 8, 53, 37)

Solution:

Step 1:

Rearrange the data set in order.

(4, 8, 9, 12, 37, 53, 66)

As there are 7 elements in the data set. The fourth element lies exactly in the center.

So, median Q2 = 12

Step 2:

Quartiles:

Lower quartile = (4, 8, 9)

Median of lower quartile Q1= 8

Upper quartile = (37, 53, 66)

Median of the upper quartile Q3= 53

Step 3:

Minimum value= 4

Maximum value= 66

So, min=4, Q1=8, Q2=12, Q3=53, max=66

Step 4:

Draw a straight line which extends in both directions.

Step 5:

Draw the modified box plots using the parameters.

Modified box plot