Question

1.2 measurements in chemistry

the length of an iron bar was measured several times. which set of data represents a precise but inaccurate measurements if the actual value is 3.9 ft?

○ 3.4, 3.5, 3.3, 3.6, 3.5, 3.4 ft

○ 3.6, 3.7, 3.8, 3.9, 4.1, 3.8 ft

○ 4.1, 4.2, 4.0, 3.9, 3.8, 3.7 ft

○ 3.9, 3.8, 3.7, 3.8, 3.9, 4.0 ft

Explanation:

Step1: Define Precision and Accuracy

Precision refers to how close the measured values are to each other. Accuracy refers to how close the measured values are to the actual value (3.9 ft here). We need a set with values close to each other (precise) but far from 3.9 ft (inaccurate).

Step2: Analyze Each Option

• Option 1 (3.4, 3.5, 3.3, 3.6, 3.5, 3.4 ft):
• These values are close to each other (range: 3.3 - 3.6, difference between max and min is 0.3).
• They are far from 3.9 ft (all less than 3.9, average around 3.45). So precise (close to each other) and inaccurate (far from 3.9).
• Option 2 (3.6, 3.7, 3.8, 3.9, 4.1, 3.8 ft):
• Values are close to 3.9 (3.6 - 4.1), so accurate (some close to 3.9) and also precise (close to each other). Not the answer.
• Option 3 (4.1, 4.2, 4.0, 3.9, 3.8, 3.7 ft):
• Values range from 3.7 - 4.2, which includes 3.9. So some are accurate, and they are spread a bit (range 0.5), but not as precise as option 1 in being far from 3.9.
• Option 4 (3.9, 3.8, 3.7, 3.8, 3.9, 4.0 ft):
• Values are very close to 3.9 (3.7 - 4.0), so accurate (close to 3.9) and precise. Not the answer.

Answer:

3.4, 3.5, 3.3, 3.6, 3.5, 3.4 ft