1. **Problem Statement:** We are given a box plot summary for girls' times in seconds with the following data: - A quarter of the girls took 32 seconds or less (lower quartile, $Q_1 = 32$). - The fastest time was 26 seconds (minimum). - A quarter of the girls took 43 seconds or more (upper quartile, $Q_3 = 43$). - The slowest time was 50 seconds (maximum). - The median time was 42 seconds ($Q_2 = 42$). We need to find: 1. Upper quartile 2. Interquartile range 3. Median 4. Range 2. **Formulas and Important Rules:** - The **upper quartile** ($Q_3$) is the value below which 75% of the data fall. - The **interquartile range (IQR)** is the difference between the upper and lower quartiles: $$IQR = Q_3 - Q_1$$ - The **median** ($Q_2$) is the middle value of the data. - The **range** is the difference between the maximum and minimum values: $$Range = Max - Min$$ 3. **Calculations:** - Upper quartile $Q_3 = 43$ seconds (given). - Interquartile range $$IQR = Q_3 - Q_1 = 43 - 32 = 11$$ seconds. - Median $Q_2 = 42$ seconds (given). - Range $$Range = Max - Min = 50 - 26 = 24$$ seconds. 4. **Explanation:** - The upper quartile is directly given as 43 seconds. - The interquartile range measures the spread of the middle 50% of the data, calculated by subtracting the lower quartile from the upper quartile. - The median is the middle value, given as 42 seconds. - The range shows the total spread of the data from fastest to slowest times. **Final answers:** - Upper quartile: 43 seconds - Interquartile range: 11 seconds - Median: 42 seconds - Range: 24 seconds