Let’s go step by step to solve each part of the worksheet.
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Problem 1:
True value = 1.24 g/mL
Measurements:
Trial #1 = 1.20 g/mL
Trial #2 = 1.22 g/mL
Trial #3 = 1.22 g/mL
a.
Accuracy comment:
Accuracy is how close the measurements are to the true value (1.24).
All three trials are a bit lower — 1.20, 1.22, 1.22 — so they’re not very close to 1.24.
→ The results are
not very accurate.
b.
Precision comment:
Precision is how close the measurements are to each other.
1.20, 1.22, 1.22 — these are all very close together.
→ The results are
very precise.
c.
What may have caused these results?
Since the measurements are consistent (precise) but consistently too low (inaccurate), this suggests a
systematic error — like a scale that’s not calibrated right, or always reading slightly low.
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Problem 2 (first one):
True value = 1.15 g/mL
Measurements:
Trial #1 = 0.95 g/mL
Trial #2 = 1.16 g/mL
Trial #3 = 1.26 g/mL
a.
Accuracy comment:
Look at how close each is to 1.15:
- 0.95 → way off
- 1.16 → very close
- 1.26 → a bit high
Average might be around 1.12, which is somewhat close, but individual values vary a lot.
→ The results are
somewhat accurate on average, but not consistently.
b.
Precision comment:
The numbers are spread out: 0.95, 1.16, 1.26 — that’s a big range.
→ The results are
not precise.
c.
What may have caused these results?
Since the measurements are all over the place (low precision) and not reliably near the true value, this suggests
random errors — maybe the student didn’t measure carefully, or the equipment was unstable, or there were mistakes in reading or recording.
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Problem 2 (second one — labeled “2” again, probably meant to be “3”):
True value = 3.75 g/mL
Measurements:
Trial #1 = 4.75 g/mL
Trial #2 = 4.76 g/mL
Trial #3 = 4.74 g/mL
a.
Accuracy comment:
All measurements are around 4.75, but the true value is 3.75 — that’s a whole 1.00 g/mL off!
→ The results are
not accurate at all.
b.
Precision comment:
4.75, 4.76, 4.74 — these are extremely close to each other.
→ The results are
very precise.
*(Note: There’s no part c for this problem in the worksheet.)*
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Final Answer:
1a. Not very accurate — all measurements are lower than the true value.
1b. Very precise — measurements are very close to each other.
1c. Likely a systematic error, like a misaligned instrument.
2a (first problem). Somewhat accurate on average, but inconsistent.
2b (first problem). Not precise — measurements vary widely.
2c (first problem). Likely random errors from careless measurement or unstable equipment.
2a (second problem). Not accurate — all measurements are about 1.00 g/mL too high.
2b (second problem). Very precise — measurements are nearly identical.
Parent Tip: Review the logic above to help your child master the concept of precision and accuracy worksheet.
