The accuracy of the measurement refers to how close the measured value is to the true or accepted value. For example, if you used a balance to find the mass of a known standard 100.00 g mass, and you got a reading of 75.95 g, your measurement would not be very accurate.
Precision refers to how close together a group of measurement actually are to each other. Precision has nothing to do with the true or accepted value of a measurement, so it is quite possible to be very precise and totally inaccurate. In many cases, when precision is high and accuracy is low, the fault can lie with the instrument. If a balance or a thermometer is not working correctly, they might consistently give inaccurate answers, resulting in high precision and low accuracy.
A dartboard analogy is often used to understand the difference between accuracy and precision. Imagine a person throwing darts, trying to hit the bullseye. The closer the dart hits to the bullseye, the more accurate the tosses are. If the person misses the dartboard with every throw, but all of their shots land close together, they can still be very precise but not accurate.
Here's another example: The TV weather forecaster says that it will be between 40 and 50 degrees today. The actual reading turns out to be 43. Thus, the forecast was accurate, but not very precise. For tomorrow, the forecast is 52.47 degrees at 4 PM. It turns out to be 39.14 degrees. This forecast was very precise, but completely inaccurate.
Problems:
1. Below is a data table produced by three groups of students who were measuring the mass of a paper clip which had a known mass of 1.0003 g. The last row is the average of their measurements.
Group 1 |
Group 2 |
Group 3 |
Group 4 |
|---|---|---|---|
| 1.01 g | 2.863287 g | 1.013251 g | 2.05 g |
| 1.03 g | 2.754158 | 1.013258 g | 0.23 g |
| 0.99 g | 2.186357 g | 1.013255 g | 0.75 g |
| 1.01 g | 2.601267 g | 1.013255 g | 1.01 g |
1a. Which group(s) are the most accurate?
b. Which group(s) are the most precise?
c. Which group is the most accurate and precise?
2a. Suppose a GPS (Global Positioning System) which measures your position on earth, is not calibrated correctly. You take 3 readings at the same place and they are all close together but 14 miles from your actual position. Explain your results in terms of precision and accuracy.
b.What is the difference in the measurements 4 vs 4.00 vs 4.00000? In terms of taking measurements, explain why we use significant figures.
