The Interquartile Range (IQR) is a statistical measure that represents the range between the first quartile (Q1) and the third quartile (Q3) of a dataset. Quartiles are values that divide a dataset into four equal parts, each containing 25% of the data. The IQR is a measure of statistical dispersion and variability within the middle 50% of the dataset.
Mathematically, the IQR is calculated as:
IQR = Q3 - Q1
Where:
- Q1 is the value below which 25% of the data falls.
- Q3 is the value below which 75% of the data falls.
The IQR is commonly used to identify potential outliers in a dataset. Outliers are data points that significantly deviate from the rest of the data and might indicate anomalies, errors, or interesting phenomena. The IQR provides a more robust measure of variability compared to the standard deviation, as it is less affected by extreme values.
To use the IQR for outlier detection:
- Calculate the IQR for the dataset.
- Define a threshold for outliers. Commonly, values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR are considered outliers.
In summary, the Interquartile Range (IQR) is a measure of variability that focuses on the middle 50% of the data, making it a useful tool for identifying outliers and understanding the spread of a dataset.
