3.2 Quartiles, Percentiles, Range and Interquartile Range We are learning to... - Understand how to find the range of a data set - Understand the purpose of interquartile range as a measure of spread - Understand quartiles as specific percentiles - Use statistical measures to compare two data sets I know I have succeeded if I can... Find the range of a set of data Find the interquartile range of a set of data - Find the percentile value of a set of data Solve reverse problems involving percentile of a set of data Apply statistical measures to solve problems Introduction: In a set of data, range = the largest value - smallest value. The interquartile range of a set of data is the difference between the upper quartile \( \left(\mathrm{Q}_{3}\right) \) an the lower quartile \( \left(\mathrm{Q}_{1}\right) \). Interquartile range \( =\mathrm{Q}_{3}-\mathrm{Q}_{1} \)
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Did you know that the concept of quartiles dates back to the early days of statistics? The term "quartile" actually originated from the French mathematician Henri Léon Lebesgue in the early 20th century. He introduced these quirky cutoffs to help statisticians understand the distribution of data better. Quartiles divide a data set into four equal parts, with each part containing a quarter of the data points, making it easier to interpret how values stack up against each other! In the real world, the interquartile range (IQR) is a superhero in disguise! Picture it as a bouncer at a club, ensuring that only a specific crowd gets in. When analyzing data sets, the IQR helps you filter out outliers that could skew results, giving you a clearer picture of the typical behavior in your data. Whether you're comparing students' test scores or the height of plants in a garden experiment, the IQR helps you understand how spread out the core values are, allowing for more accurate conclusions and decisions!