Quartile Analysis: A method to split data into quarters, revealing distribution and outliers, chosen for robustness and clarity.

Quartile analysis is a statistical method that divides a dataset into four equal parts, allowing us to understand the distribution, identify trends, and detect outliers. Here’s how quartile analysis works:

1. Definition of Quartiles:

   • The first quartile (Q1) is the median of the first half of the data.
   • The second quartile (Q2) is the median of the dataset.
   • The third quartile (Q3) is the median of the second half of the data.
   • The interquartile range (IQR) is calculated as $IQR = Q3 - Q1$.

2. Robustness:

   • Quartiles are less affected by extreme values (outliers) compared to other measures like mean and standard deviation, making them a more reliable measure for skewed distributions.

3. Clarity:

   • By breaking data into quarters, quartiles provide a clear picture of the dataset's distribution, allowing for easy identification of concentration or dispersion of values within the dataset.

4. Outlier Detection:

   • Outliers can be identified using the IQR method. Typically, any value below $Q1 - 1.5 \times IQR$ or above $Q3 + 1.5 \times IQR$ is considered an outlier.

In summary, quartile analysis offers a robust and clear method for understanding data distributions, which is crucial in many fields, including finance, healthcare, and research.