Measures of Dispersion: Range, Semi and Interquartile Range

Understanding Measures of Dispersion

Measures of dispersion help us understand how spread out the data is. They show the variability within a dataset.

Key Terms

• Range: The difference between the highest and lowest values in a dataset.
• Interquartile Range (IQR): The difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data.
• Semi-Interquartile Range: Half of the interquartile range, calculated as $\frac{\text{IQR}}{2}$.

Calculating Range

To find the range, subtract the smallest value from the largest value in the dataset:

$$\text{Range} = \text{Maximum Value} - \text{Minimum Value}$$

Calculating Interquartile Range (IQR)

The IQR is found by subtracting the first quartile (Q1) from the third quartile (Q3):

$$\text{IQR} = Q3 - Q1$$

Calculating Semi-Interquartile Range

The semi-interquartile range is half of the IQR:

$$\text{Semi-Interquartile Range} = \frac{\text{IQR}}{2}$$

Examples

Example 1: Calculating Range

Consider the dataset: 3, 7, 8, 12, 15.

Example 2: Calculating IQR and Semi-Interquartile Range

Consider the dataset: 4, 8, 10, 15, 20, 22, 25.