1. **State the problem:** We have three groups measuring the length of a board with given trial measurements. The actual length is 2.5 m. We want to determine: - Which group’s measurement is the most precise? - Which group’s measurement is the most accurate? 2. **Recall definitions:** - Precision refers to how close the measurements are to each other. - Accuracy refers to how close measurements are to the actual length (2.5 m). 3. **List data clearly:** Group 1: 1.40 m, 1.35 m, 1.37 m Group 2: 1.50 m, 1.38 m, 1.40 m Group 3: 1.38 m, 1.30 m, 1.45 m 4. **Calculate the precision for each group by finding the range (max-min):** - Group 1 range: $$1.40 - 1.35 = 0.05$$ - Group 2 range: $$1.50 - 1.38 = 0.12$$ - Group 3 range: $$1.45 - 1.30 = 0.15$$ Group 1 has the smallest range and is therefore the most precise. 5. **Calculate the average (mean) measurement for each group to assess accuracy:** - Group 1 mean: $$\frac{1.40 + 1.35 + 1.37}{3} = \frac{4.12}{3} = 1.373\,m$$ - Group 2 mean: $$\frac{1.50 + 1.38 + 1.40}{3} = \frac{4.28}{3} = 1.427\,m$$ - Group 3 mean: $$\frac{1.38 + 1.30 + 1.45}{3} = \frac{4.13}{3} = 1.377\,m$$ 6. **Compare each mean to actual length to find accuracy (difference from 2.5 m):** - Group 1 difference: $$|2.5 - 1.373| = 1.127$$ - Group 2 difference: $$|2.5 - 1.427| = 1.073$$ - Group 3 difference: $$|2.5 - 1.377| = 1.123$$ Group 2’s measurements are closest to the actual length and therefore the most accurate. **Final answers:** - Group 1 is most precise. - Group 2 is most accurate today.