Precision, Accuracy, Errors and Uncertainties | 精度、准确度、误差与不确定度

📚 Precision, Accuracy, Errors and Uncertainties | 精度、准确度、误差与不确定度

In experimental physics, measured values are never perfectly known. Two independent concepts, precision and accuracy, describe how much confidence we can place in a result. Errors are not “mistakes” but natural limitations of measurement, and uncertainties quantify the range within which the true value is expected to lie.

在实验物理中，测量值永远不可能被完全确知。精度与准确度这两个独立概念描述了我们对结果能有多少信心。误差不是 “错误”，而是测量的天然局限；不确定度则量化了真值预期所在的范围。

Understanding the difference between precision and accuracy, and being able to combine uncertainties correctly, is a core CIE A-Level Physics skill. Practical papers and theory questions both test these ideas through calculations, graphs and experimental design.

理解精度与准确度之间的区别，并能正确合成不确定度，是 CIE A-Level 物理的一项核心技能。实验卷和理论题都会通过计算、图像和实验设计来考查这些概念。

1. Precision and Accuracy Defined | 精度与准确度的定义

Precision describes the closeness of repeated measurements to one another. If a student measures the period of a pendulum five times and obtains 1.21 s, 1.22 s, 1.21 s, 1.23 s and 1.22 s, the readings are precise because the spread is small.

精度描述重复测量值彼此之间的接近程度。如果学生测量摆的周期五次，得到 1.21 s、1.22 s、1.21 s、1.23 s 和 1.22 s，这些读数精度高，因为分散范围小。

Accuracy describes the closeness of a measurement to the true or accepted value. The same pendulum may have a true period of 1.25 s, so the precise set above is precise but not accurate; it is systematically too small.

准确度描述测量值接近真值或公认值的程度。同一个摆的真实周期可能是 1.25 s，因此上述精度高的数据组并不准确；它系统性地偏小。

A low-precision but accurate set may have readings such as 1.20 s and 1.31 s that average close to 1.25 s. Precision and accuracy are therefore separate descriptions of experimental quality.

一组精度低但较准确的数据可能包含 1.20 s 和 1.31 s 等读数，其平均值接近 1.25 s。因此，精度与准确度是实验质量的两个不同描述。

2. Random Errors | 随机误差

Random errors cause repeated readings to scatter on both sides of the true value. They are usually caused by unpredictable fluctuations in the environment, by variations in reaction time, or by limitations of the observer.

随机误差使重复读数在真值两侧分散。它们通常由环境不可预测的波动、反应时间变化或观察者限制引起。

The main effect of random errors is a loss of precision. Taking many repeated readings and calculating the mean reduces the random error in the final best estimate, but it cannot remove a systematic error.

随机误差的主要影响是降低精度。多次重复读数并计算平均值可以减小最终最佳估计值中的随机误差，但不能消除系统误差。

For example, if a stopwatch is being operated by hand, each timing attempt may be slightly too long or too short. The average of many attempts is more reliable than any single reading.

例如，如果手动操作秒表，每次计时可能略微偏长或偏短。多次尝试的平均值比任何单次读数都更可靠。

3. Systematic Errors | 系统误差

A systematic error shifts every measurement by the same amount or by the same percentage in the same direction. Examples include a mass balance that reads 0.02 g too high, a stopwatch that runs slow, or a ruler with a damaged zero end.

系统误差使每个测量值沿同一方向偏移相同的量或相同的百分比。例如天平读数偏高 0.02 g、秒表走时偏慢，或直尺零端损坏。

Systematic error affects accuracy rather than precision. Since all readings are shifted together, repeating the measurement and taking the mean will not reveal the offset. The error can be identified by calibrating the instrument or by comparing with an independent method.

系统误差影响准确度而非精度。由于所有读数一起偏移，重复测量取平均值不能发现该偏差。可通过校准仪器或与独立方法比较来识别该误差。

In CIE practical work, a zero error on a vernier calliper or micrometer is a common systematic error. If the zero mark is not aligned when the jaws are closed, every reading must be corrected by adding or subtracting that fixed amount.

在 CIE 实验中，游标卡尺或千

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