![]() The middle 50% of exam scores for Class B vary by 28 points. The middle 50% of exam scores for Class A vary by only 7.5 points. Class A: IQR = Q3 – Q1 = 78.5 – 71 = 7.5Īs we observed earlier, Class A has less variability about its median.Step 1: Order the values from least to greatest. Here is the IQR for these two distributions: Find the interquartile range (IQR) of the data set. More specifically, the IQR tells us the range of the middle half of the data. The IQR is a measurement of the variability about the median. How are quartiles used to measure variability about the median? The interquartile range (IQR) is the distance between the first and third quartile marks. The 8 scores in Q3 vary by only 4 points. Compare this to the third quartile (Q3) for Class A: 25% of the scores in Class A are between 74.5 and 78.5.The eight scores in Q1 vary by 30 points. There is a lot of variability in this first quartile (Q1). For example, 25% of the scores in Class A are between 40 and 71.Notice: Some quartiles exhibit more variability in the data even though each quartile contains the same amount of data. Notice: The second quartile mark (Q2) is the median. ![]() The quartiles together with the minimum and maximum scores give the five-number summary:
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