AS Mathematics: A Guide to Experimental Methods | AS数学：实验操作指南

📚 AS Mathematics: A Guide to Experimental Methods | AS数学：实验操作指南

In AS Mathematics, the term “experiment” often refers to a planned data collection activity used to explore probability, test hypotheses or investigate statistical relationships. Unlike laboratory experiments in science, a mathematical experiment focuses on the process of randomisation, simulation and statistical inference. This guide provides a step‑by‑step framework for designing, executing and interpreting such experiments, aligning with the core statistics components of most AS Mathematics specifications.

在AS数学中，“实验”一词通常指用于探索概率、检验假设或研究统计关系的有计划的数据收集活动。与科学中的实验室实验不同，数学实验侧重于随机化、模拟和统计推断的过程。本指南提供了一个逐步框架，用于设计、执行和解读这类实验，符合大多数AS数学课程的核心统计内容。

1. What Is a Mathematical Experiment? | 什么是数学实验？

A mathematical experiment is any scenario where randomness is deliberately introduced to model a real‑world process, or where data are systematically gathered to make inferences about a population. Common examples include tossing coins, rolling dice, simulating random numbers on a calculator, and conducting sample surveys. The aim is to observe outcomes, compare them with theoretical probabilities, and quantify uncertainty.

数学实验是指任何有意引入随机性以模拟现实世界过程，或系统地收集数据以对总体进行推断的场景。常见例子包括抛硬币、掷骰子、在计算器上模拟随机数以及进行抽样调查。其目的是观察结果，将其与理论概率进行比较，并量化不确定性。

The key difference between a mathematical experiment and a purely theoretical exercise is the active collection of data, which may then be analysed using statistical tools like frequency distributions, measures of central tendency and hypothesis tests.

数学实验与纯理论练习的关键区别在于主动收集数据，然后可以使用频率分布、集中趋势度量和假设检验等统计工具对其进行分析。

2. Planning and Experimental Design | 规划与实验设计

Good experimental design ensures that the data collected is reliable and unbiased. Before gathering data, you must identify the research question or hypothesis. For instance, “Is a six‑sided die fair?” or “Does the proportion of left‑handed students in a school differ from 10%?” The design involves deciding on the number of trials, the method of data collection, and the way randomness will be incorporated.

良好的实验设计可确保收集到的数据可靠且无偏倚。在收集数据之前，你必须明确研究问题或假设。例如，“一个六面骰子是否公平？”或“学校中

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