Analysing Results | 分析实验结果

📚 Analysing Results | 分析实验结果

In CIE A-Level Physics, practical questions are not just about taking readings; they are about handling data critically. You must be able to identify errors, estimate uncertainties, draw accurate graphs, and decide whether your results support a physical law. This guide summarises the key skills needed for analysing results in papers that assess practical skills.

在 CIE A-Level 物理中，实验题不只是记录读数，而是要求批判性地处理数据。你必须能够识别误差、估计不确定度、准确绘图，并判断结果是否支持某一物理规律。本文总结实践技能考核中所需的关键结果分析能力。

1. Why result analysis matters | 为什么结果分析重要

Analysing results is central to experimental physics because a single measurement rarely proves a relationship. You need repeated readings, averages, uncertainty estimates and graphical methods to reveal patterns and test predictions. Examiners reward clear evidence of logical data handling, not just correct final values.

结果分析是实验物理的核心，因为单次测量很少能证明一种关系。你需要重复读数、平均值、不确定度估计和图解法来揭示规律并检验预测。考官看重的是清晰、有逻辑的数据处理证据，而不只是最终数值正确。

Good analysis also allows you to compare an experimental result with an accepted value and to judge whether any difference is real or simply due to experimental uncertainty. This is the foundation of a convincing practical conclusion.

好的分析还能让你将实验结果与公认值进行比较，并判断差异是真实存在还是仅仅由实验不确定度造成。这是得出有说服力的实验结论的基础。

2. Raw data, tables and significant figures | 原始数据、表格与有效数字

Record raw readings in a ruled table with headings that include the quantity and unit. Keep the number of significant figures consistent with the measuring instrument; for example, a metre rule reading might be 0.500 m, not 0.5 m, because the rule can be read to the nearest millimetre. Never change the precision of a raw reading by rounding too early.

将原始读数记录在带表格线的表格中，表头应包含物理量和单位。有效数字位数应与测量仪器一致；例如，米尺读数应为 0.500 m，而不是 0.5 m，因为米尺可读到最接近的毫米。不要过早四舍五入而改变原始读数的精度。

In a results table, calculate quantities such as T², ln T or 1/d with the same care. State column headings clearly, for example t / s, T / s, T² / s², so the meaning is unambiguous. If you process data in steps, show the processed columns rather than hiding the working.

在结果表格中，计算 T²、ln T 或 1/d 等量时同样要小心。清楚地标明列标题，例如 t / s、T / s、T² / s²，以避免歧义。如果你分步骤处理数据，应展示处理后的列，而不是隐藏计算过程。

3. Mean, range and repeatability | 平均值、极差与重复性

For repeated measurements, calculate the mean and quote it to an appropriate number of significant figures. The spread of readings can be shown by the range, which is half the interval between the largest and smallest values. If repeated values are very close, the measurement is repeatable; if they are scattered, the random uncertainty is larger.

对于重复测量，计算平均值并以适当的有效数字表示。读数的分散程度可以用极差表示，即最大值与最小值之差的一半。如果重复值非常接近，测量具有较好的重复性；如果数据分散，则随机不确定度较大。

For example, if five time readings are 1.21 s, 1.23 s, 1.20 s, 1.24 s and 1.22 s, the mean is 1.22 s and the range is (1.24 − 1.20) ÷ 2 = 0.02 s. This range gives a simple estimate of the absolute uncertainty in a single reading.

例如，若五次时间读数为 1.21 s、1.23 s、1.20 s、1.24 s 和 1.22 s，则平均值为 1.22 s，极差为 (1.24 − 1.20) ÷ 2 = 0.02 s。这个极差可给出单次读数绝对不确定度的简单估计。

4. Random and systematic errors | 随机误差与系统误差

Random errors cause readings to scatter unpredictably; repeating measurements and taking an average reduces their effect. Systematic errors, such as a zero error on a balance or a wrongly calibrated timer, shift all readings in the same direction and are not reduced by averaging.

随机误差使读数不可预测地分散；重复测量并取平均值可以减小其影响。系统误差，例如天平未归零或计时器校准错误，会使所有读数朝同一方向偏移，取平均值不能减小它。

In analysis, you should state whether an anomaly looks random or systematic. A systematic error affects accuracy, while a random error affects precision. A result can be precise but inaccurate if a systematic error is present, so both types must be considered separately.

在分析中，应判断异常值看起来是随机误差还是系统误差。系统误差影响准确度，随机误差影响精密度。如果存在系统误差，结果可能精密度高但不准确，因此必须分别考虑两类误差。

5. Uncertainty in measurements | 测量不确定度

An uncertainty is a range within which the true value is expected to lie. For an analogue instrument, the absolute uncertainty is often half the smallest division; for a digital

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