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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:

      Range=Maximum ValueMinimum 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:

      IQR=31

       

    • 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.