Dispersion

 

8.1  Dispersion 
 
  Definition  
     
 

Measures of dispersion are measurement in statistics.

It give us an idea of how values of a set of data are scattered. 

Dispersion small if the data set are quantitative measures such as range, interquartile range, variance and standard deviation 

 
     
 
 
  Tips   
     
 

The distribution of data is different. 

To understand the dispersion of data, the difference between the largest value and the smalles value is taken into consideration.

If the difference between the value is large, it indicates that the data is widely dispersed and vice versa. 

 
     
 
  Example   
     
 

The table below shows the masses, in \(kg\) of \(10\) pupils

\(52\)
\(62\)
\(12\)
\(9\)
\(8\)
\(75\)
\(44\)
\(33\)
\(19\)
\(16\)

State the difference in mass, in \(kg\) of the pupils

 
     
 

Solution

Largest mass \(= 75\)

Smallest mass \(=8\)

Difference in mass,

 \(\begin{aligned} &\space = 75-8 \\\\& = 67. \end{aligned}\)

 
 
 
  Stem and leaf plot   
     
 

It is a way to show the distributions of a set of data. 

Through stem-and-leaf plot, we can see whether the data is more likely to appear or least likely to appear. 

 
     
 
  Steps to plot the stem-and-leaf plot   
     
 

Given the data is unorganised, for example 

\(52\) \(33\)
\(25\) \(38\)
\(53\) \(53\)
\(35\) \(25\)
\(53\) \(49\)
 
     
  Thus, we cannot see the dispersion immediately. We set the tens digit as the stem and the unit digit as the leaf for the given data.  
     
 
Stem Leaf
\(2\) \(5,5\)
\(3\) \(3,5,8\)
\(4\) \(9\)
\(5\) \( 2,3,3,3\)
 
  Key \(2|5 \) means \(25\)  
 
  Dot plots   
     
 

It is a statistical chart that contains points plotted using a uniform scale.

Each point represents a value 

 
     
 
  Example of dot plot