📚 Year 8 WJEC Statistics: Practical Investigation Assessment Essentials | 八年级WJEC统计学：实践探究评估要点
In Year 8 WJEC Statistics, the practical investigation is a key assessment that tests your ability to carry out a real-world statistical enquiry. You need to plan your study, collect data, use appropriate diagrams and calculations, and evaluate your findings. This guide covers the essential skills and common pitfalls so you can approach your investigation with confidence.
在八年级WJEC统计学中，实践探究是一项关键评估，考查你开展真实世界统计调查的能力。你需要规划研究、收集数据、使用合适的图表和计算，并评估你的发现。本指南涵盖基本技能和常见误区，帮助你自信应对调查。
1. Defining the Question and Formulating Hypotheses | 明确问题与提出假设
Every statistical investigation starts with a clear, focused question. A good question is specific, measurable and relevant. For example, ‘How many hours of sleep do Year 8 students get on a school night?’ is better than ‘Do students sleep enough?’. You should also write a hypothesis – a prediction about what you expect to find. This could be a null hypothesis (no difference) and an alternative hypothesis (there is a difference). For instance, ‘There is no difference between the mean hours of sleep for boys and girls’ (H₀) versus ‘There is a difference in the mean hours of sleep for boys and girls’ (H₁).
每个统计调查都始于一个清晰、聚焦的问题。一个好问题是具体的、可测量的和相关的。例如，“八年级学生在校夜的睡眠时间是多少？”就比“学生睡眠够吗？”更好。你还应该写出假设——对预期发现的预测。可以写零假设（无差异）和备择假设（有差异）。比如，“男生和女生的平均睡眠时间没有差异”（H₀）对比“男生和女生的平均睡眠时间存在差异”（H₁）。
2. Planning Data Collection | 规划数据收集
You need to decide what data to collect and how. Primary data is gathered by you directly, for example through surveys, questionnaires or experiments. Secondary data comes from existing sources such as official statistics, books or trusted websites. Always consider the type of data: categorical (e.g. favourite subject, eye colour) or numerical. Numerical data can be discrete (countable, like number of pets) or continuous (measurable, like height or time). Your data collection sheet should be well-organised with clear column headings, units where needed and enough rows for all observations.
你需要决定收集什么数据以及如何收集。一手数据是你直接收集的，例如通过调查、问卷或实验。二手数据来自现有来源，如官方统计、书籍或可信网站。始终要考虑数据类型：分类数据（如最喜欢的科目、眼睛颜色）或数值数据。数值数据可以是离散的（可数的，如宠物数量）或连续的（可测量的，如身高或时间）。你的数据记录表应组织良好，有清晰的列标题、必要的单位和足够的行数容纳所有观测值。
3. Sampling Methods | 抽样方法
It is usually impossible to survey a whole population, so you need to select a sample. The sampling method you choose affects how well your sample represents the population. Random sampling gives every member an equal chance of being chosen and helps avoid bias. Systematic sampling selects every nth person from a list, starting at a random point. Stratified sampling divides the population into distinct groups (strata) and takes a proportional sample from each. Convenience sampling picks people who are easy to reach, which is quick but often produces biased results.
通常不可能调查整个总体，因此你需要选取一个样本。你选择的抽样方法会影响样本对总体的代表性。随机抽样使每个成员有均等的被选中的机会，有助于避免偏差。系统抽样从列表的随机起点开始，选择每第n个人。分层抽样将总体分成不同的组（层），并从每组按比例抽样。便利抽样选取容易接触到的人，这种方法快速但常常产生有偏的结果。
The table below outlines the main sampling methods and their characteristics.
| Method | English Description | 中文描述 |
|---|---|---|
| Random | Each member of the population has an equal chance of selection; reduces bias significantly. | 总体中每个成员被选中的机会均等；显著减少偏差。 |
| Systematic | Choose a random start, then select every kth item; simple but may miss periodical patterns. | 随机起点，然后每第k个选取；简单但可能错过周期规律。 |
| Stratified | Split population into strata and sample proportionally; ensures representation of each group. | 把总体分成层，按比例抽样；确保每组都有代表性。 |
| Convenience | Sample whoever is easily available; fast and cheap but often highly biased. | 选取容易找到的人；快捷廉价但通常偏差较大。 |
下表总结了主要的抽样方法及其特点。
When writing up your investigation, you must explain which method you used and why it was suitable for your study. Always discuss any potential limitations and how they might affect your conclusions.
在撰写调查时，你必须解释你使用了哪种方法以及为什么它适合你的研究。始终要讨论任何潜在的局限性，以及它们可能如何影响你的结论。
4. Organising Raw Data with Tally and Frequency Tables | 用计数表和频数表整理原始数据
Once you have collected raw data, the first step is to organise it. A tally chart allows you to record data quickly by drawing vertical strokes in groups of five – four strokes with a fifth diagonal stroke across them (||||). After completing your tallies, count them to create a frequency table. A frequency table lists each category or value alongside its frequency (the number of times it occurs). You may also need grouped frequency tables for continuous data, where you define class intervals such as 0–9, 10–19 and so on. Always give your table a clear title and label your columns with appropriate headings and units.
收集好原始数据后，第一步就是整理数据。计数表可以让你快速记录数据，把竖线画成五个一组——四竖线加一条斜线穿过（||||）。完成计数后，统计数量就得到了频数表。频数表列出每个类别或数值及其频数（出现的次数）。对于连续数据，你还需要分组频数表，定义组距，如0–9、10–19等。务必给表格一个清晰的标题，并用适当的标题和单位标注各列。
5. Displaying Data with Charts and Graphs | 用图表展示数据
Visual representations help readers see patterns and trends quickly. The type of chart you choose depends on your data. Bar charts are used for categorical or discrete data with spaces between bars. Pie charts show proportions of a whole. Line graphs show trends over time, while scatter graphs display the relationship between two continuous variables. For grouped continuous data, you can draw a histogram with bars touching. Whatever graph you plot, always label both axes clearly, use a sensible scale and give the graph a descriptive title.
图形展示能帮助读者快速看到规律和趋势。选择哪种图表取决于你的数据类型。条形图用于分类或离散数据，条形之间留有空隙。饼图展示整体的各部分比例。折线图显示随时间变化的趋势，而散点图展示两个连续变量之间的关系。对于分组连续数据，可以绘制条形紧挨着的直方图。无论画哪种图，都要清晰标注两个坐标轴，使用合理的刻度，并为图表加上描述性标题。
The following table gives a quick guide to common graphs.
下表给出了常见图表的快速指南。
| Chart Type | Best for | 最适合 |
|---|---|---|
| Bar Chart | Comparing categories or discrete counts | 比较类别或离散计数 |
| Pie Chart | Showing parts of a whole | 展示整体的组成部分 |
| Line Graph | Trend over time | 随时间变化的趋势 |
| Scatter Graph | Relationship between two continuous variables | 两个连续变量间的关系 |
| Histogram | Grouped continuous data with bars touching | 分组连续数据，条形紧接 |
When using software or drawing by hand, always check that your chart accurately reflects the data. Avoid misleading scales or 3D effects that distort proportions.
使用软件或手绘时，始终检查图表是否准确反映数据。避免误导性刻度或扭曲比例的3D效果。
6. Calculating Measures of Central Tendency | 计算集中趋势量数
Measures of central tendency describe the centre of a data set. The mean is calculated by adding all the values together and dividing by the number of values. The median is the middle value when the data is arranged in ascending order; if there are two middle numbers, take their average. The mode is the value that occurs most often. Each measure has strengths: the mean uses all data but can be affected by outliers, the median is robust against outliers, and the mode is the only measure that can be used with non-numerical data.
集中趋势量数描述数据集的中心。平均数通过将所有数值相加再除以数值的个数来计算。中位数是将数据按升序排列后的中间值；如果中间有两个数，则取它们的平均值。众数是出现次数最多的值。每种量数各有优点：平均数用了全部数据但受异常值影响，中位数不受异常值干扰，众数是唯一可用于非数值数据的量数。
Mean (x̄) = Σx ÷ n
To find the median from a frequency table, you can use the cumulative frequency. For small data sets, simple ordering is enough. The mode is simply the category or value with the highest frequency.
在频数表中找中位数，你可以使用累计频数。对于小数据集，直接排序就够。众数就是频数最高的类别或数值。
7. Calculating Measures of Spread | 计算离散程度量数
Measures of spread tell you how spread out the data are. The simplest measure is the range, which is the difference between the largest and smallest values. A larger range indicates greater variability. While the range is quick to compute, it is sensitive to outliers. At Year 8, you will mainly use the range; you might also compare the quartiles or interquartile range in more advanced investigations, but understanding the range is essential for any practical assessment.
离散程度量数告诉你数据分散的程度。最简单的量数是极差，即最大值与最小值之差。极差越大，变异性越大。虽然极差计算快捷，但它对异常值敏感。在八年级，你主要使用极差；在更高级的探究中可能会比较四分位数或四分位距，但理解极差对任何实践评估都是必要的。
Range = Maximum value – Minimum value
When writing your conclusions, always mention the range alongside the mean or median to give a fuller picture of the data. For example, two groups might have the same mean but very different ranges.
在撰写结论时，始终要把极差和平均数或中位数一起提及，以便更全面地描述数据。例如，两组数据可能平均数相同，但极差差异很大。
8. Interpreting Your Results | 解读结果
After you have calculated your statistics and drawn your graphs, it is time to interpret what the data tells you. Refer back to your original hypothesis: do the results support it or not? Use your calculations as evidence. Describe the shape of the distribution (symmetric, skewed) and link your findings to the real-world context of your investigation. Avoid simply stating numbers; explain what they mean. For instance, ‘The median screen time for boys was 3.2 hours, which is 0.8 hours higher than for girls, suggesting that boys in the sample tend to spend more time on devices.’
在计算出统计量和绘制图表后
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