# Interquartile Range: A Robust Measure of Data Dispersion

The interquartile range (IQR): IQR calculator is a widely-used measure of dispersion in statistics, providing valuable insights into the distribution of data. It is particularly useful when analyzing data sets that may contain outliers or when the data is not normally distributed. The IQR is calculated as the difference between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data. This article will explain the importance of IQR, its calculation, and its applications in real-life scenarios.

Calculating the IQR:
To calculate the IQR, we first need to determine the quartiles of the data set. Quartiles divide the data into four equal parts, with Q1 being the 25th percentile, Q2 (the median) being the 50th percentile, and Q3 being the 75th percentile. After sorting the data in ascending order, Q1 is the data point that has 25% of the data below it, and Q3 is the data point with 75% of the data below it. Once Q1 and Q3 are identified, the IQR is calculated as the difference between these two values: IQR = Q3 – Q1.

Applications of IQR:
The IQR is widely used in various fields, including finance, engineering, and social sciences. It helps identify the range within which the central portion of the data is concentrated, offering a more robust measure of dispersion compared to other methods like the range or standard deviation. In finance, the IQR can be used to analyze stock price volatility and manage investment risks. In social sciences, researchers might use the IQR to study income inequality or other demographic data that can be influenced by extreme values.