You have a group of 5 students who all measure the length of a salamander that is 17 cm long. The measurements are: 16.1 cm, 16. 2 cm, 16.1 cm, 16.2 cm, and 16.2 cm. These measurements are
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______.

Question

You have a group of 5 students who all measure the length of a salamander that is 17 cm long. The measurements are: 16.1 cm, 16. 2 cm, 16.1 cm, 16.2 cm, and 16.2 cm. These measurements are 
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______.

BlackTom AI · Accepted Answer

Precision describes how close repeated measurements are to each other, while accuracy describes how close the measurements are to the true value. A set of measurements can be precise (tight clustering) but inaccurate (systematically off from the true value), or accurate but imprecise, etc.

1. Relevant concepts
- Precision: small spread (low variability) among measurements.
- Accuracy: closeness of the mean (or typical measurement) to the true value (17.0 cm).

2. Step-by-step reasoning and calculations
Measurements: 16.1, 16.2, 16.1, 16.2, 16.2 (cm).
- Compute the mean: (16.1 + 16.2 + 16.1 + 16.2 + 16.2) = 80.8; mean = 80.8 / 5 = 16.16 cm.
- Difference from true length: 16.16 − 17.00 = −0.84 cm. The average measurement is 0.84 cm too low.
- Compute variability (population standard deviation):
  - Deviations from mean: −0.06, +0.04, −0.06, +0.04, +0.04.
  - Squared deviations: 0.0036, 0.0016, 0.0036, 0.0016, 0.0016. Sum = 0.012.
  - Variance = 0.012 / 5 = 0.0024. SD = sqrt(0.0024) ≈ 0.049 cm.
The standard deviation (~0.05 cm) is very small, showing the measurements are tightly clustered (high precision). However, the mean is far from the true value (off by 0.84 cm), so the set is not accurate.

3. Why the correct choice fits
Because the measurements are tightly clustered (low spread, high precision) but systematically lower than the true length (low accuracy), the correct description is “precise but not accurate.”

4. Why the other options are incorrect
- “Accurate and precise”: would require mean ≈ 17.0 and low spread — not true here.
- “Accurate but not precise”: would require mean ≈ 17.0 but large spread — not the case.
- “Neither accurate nor precise”: would require both large bias and large variability — here variability is small.

Final confirmation: the correct answer is “precise but not accurate,” matching the provided answer.

You have a group of 5 students who all measure the length of a salamander that is 17 cm long. The measurements are: 16.1 cm, 16. 2 cm, 16.1 cm, 16.2 cm, and 16.2 cm. These measurements are Blank ______.单项选择题

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