1. **Problem 1: Identify measures from Box Plot 1** - Minimum: 7 - 1st quartile (Q1): 10 - Median (Q2): 12 - 3rd quartile (Q3): 16 - Maximum: 19 - Range formula: $$\text{Range} = \text{Maximum} - \text{Minimum}$$ - Calculate range: $$19 - 7 = 12$$ - Interquartile range (IQR) formula: $$\text{IQR} = Q3 - Q1$$ - Calculate IQR: $$16 - 10 = 6$$ 2. **Problem 2: Identify measures from Box Plot 2** - Minimum: 26 - 1st quartile (Q1): 31 - Median (Q2): 38 - 3rd quartile (Q3): 47 - Maximum: 68 - Range: $$68 - 26 = 42$$ - IQR: $$47 - 31 = 16$$ - Fraction of data below Q1: By definition, 25% or $$\frac{1}{4}$$ of the data falls below Q1. 3. **Problem 3: Create box plot from data** - Data: 26, 26, 29, 31, 32, 34, 38, 38, 41, 47, 54, 68 - Minimum: 26 - Maximum: 68 - Median (Q2): Middle values are 34 and 38, so $$Q2 = \frac{34 + 38}{2} = 36$$ - Lower half: 26, 26, 29, 31, 32, 34 - Q1: Median of lower half is average of 29 and 31, $$Q1 = \frac{29 + 31}{2} = 30$$ - Upper half: 38, 38, 41, 47, 54, 68 - Q3: Median of upper half is average of 41 and 47, $$Q3 = \frac{41 + 47}{2} = 44$$ - Range: $$68 - 26 = 42$$ - IQR: $$44 - 30 = 14$$ 4. **Problem 4: Create box plot from data** - Data: 50, 99, 103, 246, 254, 265, 287, 315, 335, 358, 397, 427, 473, 501, 509, 625 (sorted) - Minimum: 50 - Maximum: 625 - Median (Q2): Middle values are 287 and 315, so $$Q2 = \frac{287 + 315}{2} = 301$$ - Lower half: 50, 99, 103, 246, 254, 265, 287, 315 - Q1: Median of lower half is average of 254 and 265, $$Q1 = \frac{254 + 265}{2} = 259.5$$ - Upper half: 335, 358, 397, 427, 473, 501, 509, 625 - Q3: Median of upper half is average of 473 and 501, $$Q3 = \frac{473 + 501}{2} = 487$$ - Range: $$625 - 50 = 575$$ - IQR: $$487 - 259.5 = 227.5$$ - Fraction of data between Q1 and Q2: By definition, 25% or $$\frac{1}{4}$$ of the data lies between Q1 and Q2. **Final answers:** **Problem 1:** Minimum: 7 Q1: 10 Median: 12 Q3: 16 Maximum: 19 Range: 12 IQR: 6 **Problem 2:** Minimum: 26 Q1: 31 Median: 38 Q3: 47 Maximum: 68 Range: 42 IQR: 16 Fraction below Q1: 1/4 **Problem 3:** Minimum: 26 Q1: 30 Median: 36 Q3: 44 Maximum: 68 Range: 42 IQR: 14 **Problem 4:** Minimum: 50 Q1: 259.5 Median: 301 Q3: 487 Maximum: 625 Range: 575 IQR: 227.5 Fraction between Q1 and Q2: 1/4