Measures of dispersion, also known as measures of variability or spread, provide information about how spread out or dispersed the data is. They help understand the variability or diversity of values within a dataset. Two commonly used measures of dispersion are the range and the interquartile range (IQR).
- Range: The range is the simplest measure of dispersion. It is calculated as the difference between the maximum and minimum values in a dataset. The formula for range is:
Range = Maximum value – Minimum value
The range gives an idea of the total spread of the data. However, it is sensitive to extreme values and may not provide a complete picture of the variability if outliers are present.
- Interquartile Range (IQR): The interquartile range is a measure of dispersion that is based on quartiles. It represents the range of values within the middle 50% of the dataset. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The formula for the interquartile range is:
IQR = Q3 – Q1
The IQR is more robust to outliers than the range and provides a better representation of the spread of the central portion of the data.
Both the range and interquartile range are useful measures of dispersion, but the interquartile range is often preferred when the data contains outliers or extreme values.