Analysis of Experimental Data in CIE A-Level Physics | CIE A-Level 物理实验数据分析

📚 Analysis of Experimental Data in CIE A-Level Physics | CIE A-Level 物理实验数据分析

In CIE A-Level Physics, data analysis is a core skill assessed especially in Paper 5 (Planning, Analysis and Evaluation). It is not just about plugging numbers into formulas; it requires you to identify and quantify errors, choose the most informative graph, extract values from gradients and intercepts, and judge whether your data actually support the expected physical relationship.

在 CIE A-Level 物理中，数据分析是一项核心技能，尤其在 Paper 5（实验规划、分析与评估）中考查。它不仅仅是把数字代入公式，还要求你识别并量化误差、选择最有信息量的图像、从斜率和截距中提取数值，并判断数据是否真正支持预期的物理关系。

1. Types of Data and Errors | 数据类型与误差

Raw data are the readings you record directly from instruments. Processed data are quantities calculated from raw readings, such as averages, squares, or reciprocals. Errors are usually divided into random errors and systematic errors.

原始数据是你直接从仪器记录下来的读数。处理数据是由原始读数计算出来的量，例如平均值、平方或倒数。误差通常分为随机误差和系统误差。

Random errors cause readings to scatter unpredictably about the true value. They can be reduced by taking repeated measurements and using the mean. Systematic errors cause all readings to be shifted in the same direction, often due to poor calibration or a zero error, and they cannot be reduced by repetition.

随机误差使读数在真值附近不可预测地散布。可以通过多次测量并取平均值来减小。系统误差使所有读数朝同一方向偏移，通常由校准不良或零点误差引起，重复测量无法减小系统误差。

2. Recording Data with Absolute Uncertainties | 记录数据与绝对不确定度

Every measured value should be written with an absolute uncertainty. For a single reading on a digital instrument, the absolute uncertainty is at least ± the smallest scale division, or the manufacturer’s stated accuracy if larger. For an analogue instrument, it is usually half the smallest scale division.

每个测量值都应写出绝对不确定度。对于数字仪器的单次读数，绝对不确定度至少为最小分度值，或制造商标称的准确度（如果更大）。对于模拟仪器，通常取最小分度值的一半。

For repeated readings, the best estimate is the mean, and a simple estimate of the absolute uncertainty is half the range: (maximum − minimum) ÷ 2. You should record this as value ± uncertainty with a consistent unit.

对于重复读数，最佳估计值是平均值，绝对不确定度的一个简单估计是半极差：（最大值 − 最小值）÷ 2。记录时应写成 数值 ± 不确定度，并保持单位一致。

3. Percentage Uncertainties and Propagation | 百分比不确定度与传递

The percentage uncertainty is found from:

百分比不确定度由下式得出：

percentage uncertainty = (absolute uncertainty ÷ measured value) × 100%

百分比不确定度 = (绝对不确定度 ÷ 测量值) × 100%

When two quantities are added or subtracted, absolute uncertainties add in quadrature or as a simple sum for a conservative estimate. The simple sum rule is often accepted at A-Level:

当两个量相加或相减时，绝对不确定度可以按平方根合成，或采用更保守的简单相加。A-Level 中通常接受简单相加规则：

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