Accuracy And Precision Worksheet With Answers

What Is Accuracy and Precision?

You measure something three times and get three different numbers. Practically speaking, or you measure something three times and get the exact same wrong answer every time. Sound familiar? If you've ever worked through a lab experiment or graded a set of data, you know the frustration of not knowing whether your results are good, bad, or somewhere in between. That's where accuracy and precision come in — and honestly, these two concepts are the ones most students mix up.

Here's the short version. In real terms, accuracy is about how close your measurement is to the true or accepted value. A dartboard makes this crystal clear. That's why if your darts all land in the same spot but it's the wrong spot, you're precise but not accurate. Precision is about how close your measurements are to each other. That's why you've got both. And if they're clustered right on the bullseye? If they land all over the board but average out near the bullseye, you're accurate but not precise. That's the sweet spot.

This is the bit that actually matters in practice Simple, but easy to overlook..

Why Accuracy and Precision Matter

So why does this distinction actually matter? In a classroom setting, it's the difference between a solid lab report and one that gets marked down. But in the real world, the stakes get higher fast. Think about it: think about manufacturing — if a machine cuts parts that are consistently off by two millimeters, those parts are precise but not accurate, and the final product won't work. Think about medicine — dosing a drug requires both accuracy (hitting the right amount) and precision (getting that same amount every single time) Not complicated — just consistent..

The official docs gloss over this. That's a mistake Worth keeping that in mind..

The concept also shows up everywhere from cooking to engineering to sports analytics. When someone says a thermometer is "accurate to within one degree," they're telling you something specific about how much trust you can place in a single reading. Day to day, when they say a scale is "precise to 0. On top of that, 01 grams," they're talking about its repeatability. Understanding the difference helps you evaluate instruments, interpret data, and catch errors before they snowball Easy to understand, harder to ignore..

This is where a lot of people lose the thread.

How to Tell the Difference

Accuracy in Practice

Accuracy answers the question: "Am I hitting the target?" It's a measure of systematic error — the gap between your result and the known or accepted value. In a worksheet context, you'll usually see accuracy expressed as a percentage error.

Percentage Error = |Accepted Value − Measured Value| / Accepted Value × 100%

A lower percentage error means higher accuracy. Day to day, if the accepted boiling point of water is 100°C and you measure it as 97°C, your percentage error is 3%. Not perfect, but you're in the ballpark Worth knowing..

Precision in Practice

Precision answers a different question: "Are my results consistent?" It's about random error — the scatter or spread in your data set. You measure precision using things like the range (the difference between the highest and lowest values), the standard deviation, or simply by looking at how tightly grouped your numbers are No workaround needed..

Here's a scenario that trips people up. 8 g, 10.Practically speaking, imagine you weigh a sample five times and get these readings: 10. 0 g, 10.Here's the thing — 5 g, 12. On top of that, 0 g, so your accuracy could be decent, but the spread is huge — your precision is poor. That's why 9 g, 10. But if the true mass is 12.Still, the average might be close to 12. Because of that, 1 g, 10. 2 g, 9.In practice, 3 g, 13. Practically speaking, 9 g. Now flip it: you get readings of 11.That's why 1 g, 11. Still, 1 g. On top of that, 0 g, your accuracy is terrible. So those numbers are close together, so the precision is good. See how they're independent of each other?

Accuracy and Precision Worksheet with Answers

We're talking about where it all comes together. So naturally, a worksheet on accuracy and precision gives you the chance to test your understanding with real numbers. Below you'll find a set of practice questions that cover the key ideas — calculating percentage error, identifying which data sets are accurate, precise, both, or neither, and interpreting measurements in context.

Worksheet Questions

Question 1. A student measures the length of a metal rod five times and records the following values: 25.4 cm, 25.3 cm, 25.5 cm, 25.4 cm, 25.3 cm. The accepted length is 25.0 cm. Are the measurements accurate, precise, both, or neither? Explain your reasoning Small thing, real impact..

Question 2. In a chemistry lab, the true mass of a substance is 50.0 g. A group of students records the following masses: 49.8 g, 50.1 g, 50.0 g, 49.9 g, 50.2 g. Calculate the average measured value and the percentage error. How would you describe the accuracy and precision of this data set?

Question 3. Another group measures the same substance and records: 47.2 g, 53.1 g, 48.9 g, 51.5 g, 49.8 g. Calculate the average and the percentage error. Describe the accuracy and precision.

Question 4. A thermometer reads 98.6°F, 98.6°F, 98.6°F, and 98.6°F when placed in a liquid that is known to be at 100.0°F. Evaluate the accuracy and precision.

Question 5. A GPS device records your position five times while you're standing still. The coordinates are: (40.7128° N, 74.0060° W), (40.7130° N, 74.0058° W), (40.7127° N, 74.0062° W), (40.7129° N, 74.0061° W), (40.7131° N, 74.0059° W). The actual location is (40.7135° N, 74.0055° W). Discuss the accuracy and precision of the GPS readings Small thing, real impact..

Question 6. A scale is used to weigh a standard 100.0 g calibration mass. The readings are: 102.1 g, 102.3 g, 102.0 g, 102.2 g, 102.1 g. What is the average reading? What is the percentage error? Are the readings accurate? Are they precise?

Question 7. True or False: A set of measurements can be precise but not accurate. Justify your answer with a quick example.

Question 8. True or False: High accuracy always means high precision. Explain why or why not.

Answer Key with Explanations

**Answer

Answer Key with Explanations

Question 1

Data: 25.4 cm, 25.3 cm, 25.5 cm, 25.4 cm, 25.3 cm
Accepted value: 25.0 cm

• Precision: The five values cluster tightly between 25.3 cm and 25.5 cm, indicating excellent repeatability.
• Accuracy: Every reading is consistently above the true value by 0.3–0.5 cm; the systematic bias shows the method is not centered on the accepted length.
• Conclusion: Precise but not accurate.

Question 2

Data: 49.8 g, 50.1 g, 50.0 g, 49.9 g, 50.2 g
True mass: 50.0 g

Average:
[ \bar m = \frac{49.8+50.1+50.0+49.9+50.2}{5}=50.0\text{ g} ]

Percentage error:
[ %E = \frac{|50.0-50.0|}{50.0}\times100% = 0.0% ]

• Precision: The spread (50.0 g ± 0.2 g) is very small; measurements repeat well.
• Accuracy: The mean matches the true value exactly, so the data are also accurate.
• Conclusion: Both accurate and precise.

Question 3

Data: 47.2 g, 53.1 g, 48.9 g, 51.5 g, 49.8 g

Average:
[ \bar m = \frac{47.2+53.1+48.9+51.5+49.8}{5}=50.1\text{ g} ]

Percentage error:
[ %E = \frac{|50.1-50.0|}{50.0}\times100% = 0.2% ]

• Precision: The values range from 47.2 g to 53.1 g, a spread of 5.9 g—quite large, indicating poor repeatability.
• Accuracy: The mean is close to the true value (0.2 % error), but the large spread means the method is not reliable.
• Conclusion: Accurate but not precise.

Question 4

Readings: 98.6 °F, 98.6 °F, 98.6 °F, 98.6 °F
Known temperature: 100.0 °F

• Precision: All four readings are identical; the instrument is highly precise.
• Accuracy: Each reading is 1.4 °F below the true value, a systematic error.
• Conclusion: Precise but not accurate.

Question 5

GPS coordinates (rounded to 4 decimals):

• (40.7128 N, 74.0060 W)
• (40.7130 N, 74.0058 W)
• (40.7127 N, 74.0062 W)
• (40.7129 N, 74.0061 W)
• (40.7131 N, 74.0059 W)

Actual location: (40.7135 N, 74.0055 W)

Precision: The five reported positions cluster within 0.0004 ° latitude and 0.0005 ° longitude – a tight grouping, indicating good repeatability.

Accuracy: The cluster is shifted about 0.0007 ° south and 0.0004 ° east relative to the true point, reflecting a consistent offset Took long enough..

• Conclusion: Precise but not fully accurate.

Question 6

Readings: 102.1 g, 102.3 g, 102.0 g, 102.2 g, 102.1 g
Calibration mass: 100.0 g

Average:
[ \bar m = \frac{102.1+102.3+102.0+102.2+102.1}{5}=102.14\text{ g} ]

Percentage error:
[ %E

Percentage error: [ %E = \frac{|102.14 - 100.0|}{100.0} \times 100% = 2.14% ]

• Precision: The values cluster tightly between 102.0 g and 102.3 g, indicating good repeatability.
• Accuracy: The mean is significantly higher than the true value (2.14% error), suggesting a systematic bias in the instrument or method.
• Conclusion: Precise but not accurate.

Final Conclusion

The analysis of these datasets illustrates the distinction between precision (consistency of measurements) and accuracy (closeness to the true value). Systems can exhibit high precision but low accuracy due to systematic errors, as seen in the temperature and GPS examples. Conversely, accuracy without precision (e.g., Question 3) highlights the impact of random errors. Both attributes are critical for reliable measurements, emphasizing the need to address both random and systematic uncertainties in experimental design Less friction, more output..