Measures of dispersion, also known as measures of variability, provide information about how spread out or dispersed the values in a dataset are. Two common measures of dispersion are the range and the interquartile range (IQR):

1. Range:
   • The range is a simple measure of dispersion and is calculated as the difference between the maximum and minimum values in a dataset.
   • Mathematically, it can be expressed as:
     
     $\text{Range}=\text{Maximum Value}-\text{Minimum Value}$

      

     Range=Maximum Value−Minimum Value

   • The range is straightforward to compute but can be highly influenced by outliers. It provides a basic understanding of how widely the data values vary from each other.
2. Interquartile Range (IQR):
   • The interquartile range (IQR) is a more robust measure of dispersion that is less affected by extreme values (outliers) than the range.
   • It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) and represents the spread of the middle 50% of the data.
   • Mathematically, it can be expressed as:
     
     $\text{IQR}=�3-�1$

      

     IQR=Q3−Q1

   • The IQR is particularly useful for identifying the central range of the data and is commonly used in box plots to visualize data spread.

How to Calculate the IQR: To calculate the IQR, follow these steps:

1. Calculate the first quartile (Q1) and the third quartile (Q3) of the dataset.
2. Find the difference between Q3 and Q1 to obtain the IQR.

The IQR is a useful measure of dispersion because it is not influenced by extreme values in the same way the range is. It provides a better understanding of the spread of data while focusing on the middle 50% of the observations, making it less sensitive to outliers.