1. The problem is to understand the difference between a quartile and a percentile. 2. Quartiles divide a data set into four equal parts, each containing 25% of the data. The three quartiles are: - First quartile ($Q_1$): 25th percentile - Second quartile ($Q_2$): 50th percentile (also the median) - Third quartile ($Q_3$): 75th percentile 3. Percentiles divide a data set into 100 equal parts, each containing 1% of the data. For example, the 20th percentile is the value below which 20% of the data fall. 4. In summary, quartiles are specific percentiles: $Q_1 = 25^{th}$ percentile, $Q_2 = 50^{th}$ percentile, and $Q_3 = 75^{th}$ percentile. 5. Both quartiles and percentiles help describe the distribution of data by indicating the relative standing of values within the data set.