The interquartile range (IQR) is a measure of statistical dispersion, representing the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.
Steps to Calculate Interquartile Range:
- Arrange the Data: Order your dataset from smallest to largest.
- Find the Median: Locate the middle value of your dataset. This is your second quartile (Q2), also known as the median.
- Identify Q1 and Q3:
- The first quartile (Q1) is the median of the lower half of the dataset (excluding Q2 if the dataset has an odd number of values).
- The third quartile (Q3) is the median of the upper half of the dataset (excluding Q2 if the dataset has an odd number of values).
- Calculate IQR: Subtract Q1 from Q3: IQR = Q3 - Q1.
Example:
Let's say we have the following dataset: 2, 4, 5, 7, 8, 9, 11, 12, 14.
- Arrange the Data: Already arranged.
- Find the Median: The median is 8 (the middle value).
- Identify Q1 and Q3:
- Q1 is 5 (the median of the lower half: 2, 4, 5, 7).
- Q3 is 11 (the median of the upper half: 9, 11, 12, 14).
- Calculate IQR: IQR = 11 - 5 = 6.
Practical Insights:
- The IQR represents the spread of the middle 50% of the data.
- A larger IQR indicates greater variability in the data.
- The IQR is less sensitive to outliers compared to the range.
