Lecture Notes: Statistical Concepts and Practice Problems Part 4: Quartiles, Range, and Box-and-Whisker Plot Definitions • Range: Difference between the maximum and minimum values. • Quartiles: – Q1 : First quartile (25th percentile) – Q2 : Median (50th percentile) – Q3 : Third quartile (75th percentile) • Interquartile Range (IQR): IQR = Q3 − Q1 • Box-and-Whisker Plot: A visual representation of the data distribution using quartiles, whiskers, and outliers. Box-and-Whisker Plot for the Data Data Distribution Box-and-Whisker Plot for Yoga Class Attendance 0 2 4 6 8 10 12 14 Number of Attendees 1 16 18 20 Plot Details • Median (Q2 ): 8 • First Quartile (Q1 ): 6 • Third Quartile (Q3 ): 9 • Interquartile Range (IQR): 3 • Whiskers: 2 (Lower) and 12 (Upper) • Outlier: 18 (plotted as a point) Other Concepts Part 1: Measures of Central Tendency • Mean (Average): The sum of all values divided by the number of values. Pn xi x̄ = i=1 n • Median: The middle value of a sorted data set. • Mode: The value(s) that occur most frequently in the data set. • Outliers: Data points that differ significantly from others. Part 2: Percentiles • Percentiles divide data into 100 equal parts. • Formula for a specific percentile p: R= p (n + 1) 100 Part 3: Interval Data • For grouped data, the mean is calculated as: P fi mi x̄ = P fi where fi is the frequency and mi is the midpoint. 2

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