Quartile Deviation

Quartile Deviation

Definition:

• Quartile deviation (Qd) is a measure of dispersion that estimates the spread of data around the median.
• It is half of the inter-quartile range (IQR), which encompasses the middle 50% of data values in a distribution.

Calculation:

• Formula: $Qd=\frac{Q3-Q1}{2}$​
  • Q1: First quartile (25th percentile)
  • Q3: Third quartile (75th percentile)

Interpretation:

• Quartile deviation focuses on the central 50% of the data, ignoring extreme values.
• It is less influenced by outliers compared to the range, making it useful for skewed distributions or data with outliers.
• Changes in the scale of data affect quartile deviation proportionally.

Properties:

• Semi Inter-Quartile Range: Since Qd is half of IQR, it is also known as the semi inter-quartile range.
• Suitability: Ideal for comparing the spread of distributions with different scales or units.
• Coefficient of Quartile Deviation: Provides a dimensionless measure to compare dispersion across different datasets.

Coefficient of Quartile Deviation:

• Formula: Coefficient of Quartile Deviation = $\frac{Q3-Q1}{Q3+Q1}\times 100$
• It standardizes quartile deviation for comparison across distributions.

Use Cases:

• Statistical Analysis: Used in fields where extreme values can skew results, such as economics or biology.
• Comparative Analysis: Helps understand how spread differs between groups or datasets.
• Robustness: Less sensitive to outliers compared to range or standard deviation.

Conclusion: 

Quartile deviation provides a robust measure of dispersion by focusing on the middle portion of data, making it particularly useful in situations where extreme values can distort other measures. It offers insights into the spread of data around the median, offering a balanced view of variability in a dataset.