Understanding the Interquartile Range (IQR)
Hello, everyone! Sorry for the delay in posting. Let's continue our statistics exploration. In our last post, we covered standard deviation and how it measures variability around the mean. Today, we’re diving into another useful measure of spread: the Interquartile Range (IQR). This metric zeroes in on the middle portion of the data, offering a clearer picture of central distribution while sidestepping the impact of outliers. What Is the Interquartile Range (IQR)? The Interquartile Range (IQR) captures the spread of the middle 50% of data. Unlike variance or standard deviation, which involve all data points, the IQR focuses on the range between the first and third quartiles (Q1 and Q3). By ignoring the extreme values on either end, the IQR is especially helpful in understanding data with outliers or skewed distributions. In other words, the IQR helps us see where most of the central data points lie, offering a more robust view of spread that’s less influenced by unusually high or low values. How to Calculate the IQR The IQR is the difference between the third quartile (Q3) and the first quartile (Q1): IQR = Q3 − Q1 Breaking Down the Quartiles: - Q1 (First Quartile): The median of the lower half of the dataset, marking the point below which 25% of data points lie. - Q3 (Third Quartile): The median of the upper half, showing the point below which 75% of data points lie. Example: Student Scores (on a Scale of 1 to 10) Let’s look at an example of IQR using student test scores ranging from 1 to 10: Scores = 2, 3, 4, 5, 6, 6, 7, 8, 9, 10 Find Q1 (first quartile): The lower half of the dataset (2, 3, 4, 5, 6) has a median value of 4. Find Q3 (third quartile): The upper half (6, 7, 8, 9, 10) has a median of 8. Calculate the IQR: IQR = 8 − 4 = 4 This IQR tells us that the central 50% of scores lie between 4 and 8 on the 1-10 scale, providing insight into where the middle values are concentrated. While the range (4 to 8) defines the boundaries of the middle 50%, the IQR (4) quantifies how spread out those values are, offering a clearer picture of the data's variability.