📚 Accuracy in A-Level Physics | A-Level 物理中的准确度
In AQA A-level Physics, 'accuracy' describes how close a measured value is to the true or accepted value. It is not the same as precision, and it is linked directly to systematic errors, calibration and uncertainty analysis. This article explains the key ideas you need for practical work and exam questions.
在 AQA A-level 物理中，'准确度' 描述测量值与真值或公认值的接近程度。它与精确度不同，并且与系统误差、校准和不确定度分析直接相关。本文将解释你需要在实验工作和考试题中掌握的关键概念。
1. What Accuracy Means | 准确度的含义
ccepted reference quantity, such as g = 9.81 m s⁻² or the specific heat capacity of water.
准确度是单个测量值与真值之间的接近程度。真值可以是公认的参考量，例如 g = 9.81 m s⁻² 或水的比热容。
An accurate result has small systematic error. It does not necessarily mean the result is precise; a single reading can be accurate by careful calibration or by chance.
准确的结果系统误差很小。这并不一定意味着结果很精确；单次读数可能因仔细校准或偶然因素而准确。
In AQA mark schemes, accuracy is judged by comparing the experimental mean to an accepted value, often using percentage difference.
在 AQA 评分标准中，准确度通过将实验平均值与公认值进行比较来判断，通常使用百分比差异。
2. Accuracy vs Precision | 准确度与精确度的区别
Precision refers to how closely repeated measurements agree with one another. It reflects random uncertainty, not closeness to the true value.
精确度是指重复测量值彼此之间的一致程度。它反映随机不确定度，而不是与真值的接近程度。
A set of results can be precise but inaccurate if every reading is affected by the same systematic error. Conversely, a set can be accurate on average but imprecise if random errors cause wide scatter.
如果每个读数都受到同一系统误差的影响，一组结果可以精确但不准确。相反，如果随机误差导致读数分散很宽，一组结果可以在平均意义上准确但不精确。
| Scenario | Meaning |
|---|---|
| Precise but inaccurate | 精确但不准确 | Small scatter, far from true value | 离散小，但远离真值 |
| Accurate but imprecise | 准确但不精确 | Mean close to true value, large scatter | 平均值接近真值，离散大 |
| Accurate and precise | 准确且精确 | Small scatter and mean close to true value | 离散小且平均值接近真值 |
Related terms: repeatability is precision under the same conditions; reproducibility is precision when conditions change, such as a different experimenter or instrument.
相关术语：重复性是在相同条件下测量的精确度；再现性是条件改变（例如不同实验者或仪器）时的精确度。
3. Systematic and Random Errors | 系统误差与随机误差
Random errors cause repeated readings to scatter unpredictably. They affect precision. Their effect can be reduced by taking many repeats and using the mean.
随机误差导致重复读数不可预测地分散。它们影响精确度。通过多次重复并取平均值可以减小其影响。
Systematic errors shift all readings in the same direction, for example a zero error or a wrong calibration. They affect accuracy, and repeating measurements does not reduce them.
系统误差使所有读数向同一方向偏移，例如零误差或错误校准。它们影响准确度，重复测量并不能减小它们。
Identifying the type of error is a common AQA task: if the mean is close to the true value but readings scatter, random error dominates; if the scatter is small but the mean is far from the true value, systematic error dominates.
识别误差类型是 AQA 常见任务：如果平均值接近真值但读数分散，随机误差占主导；如果分散小但平均值远离真值，系统误差占主导。
4. Resolution and Reading Uncertainty | 分辨率与读数不确定度
Resolution is the smallest change an instrument can display or detect. A ruler with millimetre divisions has a resolution of 1 mm.
分辨率是仪器能够显示或检测到的最小变化。带有毫米刻度的尺子分辨率为 1 mm。
s ± the smallest displayed digit, though AQA questions often state the uncertainty to use.
对于模拟刻度，读数不确定度通常取最小分度值的一半。对于数字仪器，通常取最小显示位数，不过 AQA 题目通常会说明要使用的不确定度。
If a measurement is repeated, the uncertainty can be estimated from the half-range: (max - min)/2. This gives an indication of random scatter.
如果重复测量，不确定度可以用半范围来估计：(最大值 - 最小值) ÷ 2。这可以指示随机分散程度。
half-range uncertainty = (maximum reading - minimum reading) ÷ 2
5. Absolute, Fractional and Percentage Uncertainty | 绝对、相对与百分比不确定度
nty is the uncertainty in a measurement expressed in the same unit, such as 25.0 ± 0.2 cm.
绝对不确定度是以相同单位表示的测量不确定度，例如 25.0 ± 0.2 cm。
Fractional uncertainty is absolute uncertainty divided by the measured value. Percentage uncertainty is the fractional uncertainty multiplied by 100%.
相对不确定度是绝对不确定度除以测量值。百分比不确定度是相对不确定度乘以 100%。
fractional uncertainty = absolute uncertainty ÷ measured value
percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%
e: a length is measured as 50.0 ± 0.2 cm. The percentage uncertainty is (0.2 ÷ 50.0) × 100% = 0.40%.
示例：某长度测量为 50.0 ± 0.2 cm。百分比不确定度为 (0.2 ÷ 50.0) × 100% = 0.40%。
6. Combining Uncertainties: Addition and Subtraction
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