Year 9 AQA Statistics: Statistical Investigation Report Writing Framework and Model Answer | 九年级AQA统计：论文写作框架与范文

📚 Year 9 AQA Statistics: Statistical Investigation Report Writing Framework and Model Answer | 九年级AQA统计：论文写作框架与范文

In Year 9 AQA Statistics, mastering the art of writing a statistical investigation report is a fundamental skill. This type of academic paper requires you to follow a clear framework, from formulating a hypothesis to presenting data and drawing evidence-based conclusions. This article will guide you through each section of the report, provide a detailed model answer, and highlight how to meet AQA’s assessment objectives.

在九年级 AQA 统计课程中，掌握统计调查报告的写作是一项核心技能。这种学术论文需要你遵循一个清晰的框架，从提出假设到呈现数据，再到基于证据得出结论。本文将带你了解报告的每一个部分，提供一篇详细的范文，并指出如何满足 AQA 的评估目标。

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1. Understanding the Statistical Enquiry Cycle (PPDAC) | 理解统计调查周期 (PPDAC)

Every good statistical report is built around the PPDAC cycle: Problem, Plan, Data, Analysis, Conclusion. This framework ensures your investigation is structured and logical. You begin by identifying a problem or question, planning how to collect data, gathering and processing that data, analysing it with appropriate measures and visualisations, and finally drawing a conclusion that refers back to your original question.

每份优秀的统计报告都围绕 PPDAC 周期构建：问题 (Problem)、计划 (Plan)、数据 (Data)、分析 (Analysis)、结论 (Conclusion)。这个框架确保你的调查结构清晰、逻辑合理。你首先要明确一个问题，接着规划如何收集数据，然后收集并处理数据，使用恰当的指标和可视化方法进行分析，最后得出结论并回扣最初的问题。

In the AQA specification, examiners expect you to demonstrate understanding of this cycle. Your written report should mirror these stages, showing that you have thought carefully about each step rather than just performing calculations in isolation.

在 AQA 考纲中，考官期望你展现出对这个周期的理解。你的书面报告应该反映出这些阶段，表明你认真思考了每一步，而不是孤立地做计算。

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2. Defining the Problem and Hypothesis | 定义问题和假设

The first section of your report must clearly state the statistical problem you are investigating. Frame it as a question, for example: ‘Is there a relationship between the number of hours Year 9 students spend on mobile phones and the number of hours they sleep?’ Then translate this into a testable hypothesis, such as: ‘Students who use mobile phones for more hours per day tend to have fewer hours of sleep.’

报告的第一部分必须清晰陈述你所研究的统计问题。把问题表述成一则疑问，例如：“九年级学生每天使用手机的小时数与他们的睡眠小时数之间是否存在关系？”然后把它转化为可检验的假设，比如：“每天使用手机时间越长的学生，往往睡眠时间越短。”

Your hypothesis should be directional if you predict a positive or negative association, or non-directional if you are simply testing for a difference or relationship. This clarity will guide your entire investigation.

如果你预测一种正向或负向的关联，你的假设应当有方向；如果你只检验某种差异或关系，则是无方向的。这种明确性将为整个调查提供指引。

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3. Planning Data Collection | 规划数据收集

Explain how you will collect data to test your hypothesis. For a Year 9 investigation, you might use a questionnaire with questions about typical daily phone usage and average sleep duration. Describe your sampling method – for instance, simple random sampling of 20 Year 9 students from your school register to minimise bias.

解释你将如何收集数据来检验假设。对于九年级的调查，你可以使用一份问卷，询问每日手机的典型使用时长和平均睡眠时长。描述你的抽样方法——例如，从学校名册中对 20 名九年级学生进行简单随机抽样，以减少偏倚。

Also consider the variables: your independent variable is phone use (hours), and your dependent variable is sleep (hours). Mention that you will control for confounding factors by ensuring all responses are collected during a normal school week without exam stress.

还要考虑变量：自变量是手机使用时间（小时），因变量是睡眠时间（小时）。提及你将通过确保所有回答都在没有考试压力的正常上课周内收集，来控制混杂因素。

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4. Collecting Data | 收集数据

This part is practical. Describe how the data were actually gathered. For instance, you distributed the questionnaire during form time and collected 18 valid responses after removing two incomplete forms. Emphasise anonymity and honesty to maintain ethical standards.

这一部分很贴合实际。描述数据是如何实际收集的。例如，你在班主任指导课时发放了问卷，在剔除两份不完整的表格后，得到了 18 份有效回复。强调匿名性和如实作答，以维护伦理规范。

Present the raw data in a neatly formatted table. Use clear headings and units. This demonstrates good data handling before any processing takes place.

用格式整洁的表格展示原始数据。使用清晰的标题和单位。这表明在进行任何处理之前，你已经妥善整理了数据。

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5. Processing and Presenting Data | 处理与呈现数据

Once you have raw data, you must process it into forms that are easy to interpret. This includes calculating summary statistics and creating visual representations. Begin by organising the data into ordered lists and then constructing frequency tables or grouped frequency tables if the range is wide.

获得原始数据后，你必须把它处理成易于解读的形式。这包括计算汇总统计量和创建可视化呈现。首先将数据整理为有序列表，然后构建频数表，如果极差较大则构建分组频数表。

Visual presentation is key. You might plot a scatter graph to show the relationship between two numerical variables, or draw a bar chart for comparing categories. In an investigation about phone use and sleep, a scatter graph with a line of best fit is ideal. Always label your axes and give your graph a clear title.

可视化呈现非常关键。你可以绘制散点图来展示两个数值变量之间的关系，或者绘制条形图来比较类别。在手机使用与睡眠的调查中，理想的选择是绘制散点图并添加最佳拟合线。务必标记坐标轴，并为图形添加清晰的标题。

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6. Calculating Statistical Measures | 计算统计指标

Now calculate measures of central tendency and spread. For your phone use and sleep data, compute the mean using the formula:

现在计算集中趋势和离散程度的指标。对于手机使用和睡眠数据，使用下面的公式计算平均值：

Mean = (Σx) ÷ n

where Σx is the sum of all values and n is the number of data points. Also find the median by locating the middle value in the ordered list, and the mode if a value repeats frequently. To describe spread, calculate the range (maximum – minimum) and the interquartile range (IQR) by subtracting the lower quartile from the upper quartile.

其中 Σx 是所有数值的总和，n 是数据点的个数。还要找出中位数，即在排序后的列表中处于中间位置的值；如果有数值频繁重复，则找出众数。为了描述离散程度，计算极差（最大值减最小值）和四分位距 (IQR)，即上四分位数减去下四分位数。

These measures allow you to compare the distributions. For example, you might notice that the mean sleep duration for students with low phone use is over 8 hours, while for high phone use it drops below 7 hours. This begins to reveal the pattern in your data.

这些指标让你能够比较分布情况。例如，你可能会注意到，手机使用时间短的学生平均睡眠时长超过 8 小时，而手机使用时间长的学生则降至 7 小时以下。这便开始揭示数据中的模式。

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7. Analysing and Interpreting Results | 分析与解读结果

Analysis goes beyond numbers – it explains what the numbers mean in context. Comment on the scatter graph: if points show a downward pattern from left to right, you have a negative correlation. The line of best fit helps to quantify this relationship. Calculate the equation of the line if required, using a graphical method or by selecting two points on the line to find gradient and intercept.

分析不止于数字——它要解释这些数字在具体情境中意味着什么。对散点图进行评论：如果点从左到右呈现下降趋势，则存在负相关。最佳拟合线有助于量化这种关系。如果需要，可以使用图形法计算直线的方程，或选取线上的两点求出斜率和截距。

Use your calculated statistics to support the interpretation. For instance, ‘The mean sleep duration for the five students with the highest phone use was 6.4 hours, compared to 8.1 hours for the five with the lowest phone use. This difference of 1.7 hours suggests a substantial negative association.’ Refer back to your original hypothesis.

运用计算出的统计量来支撑解读。例如，“手机使用时间最长的五名学生的平均睡眠时长为 6.4 小时，而使用时间最短的五名学生为 8.1 小时。这 1.7 小时的差异表明存在明显的负相关。”要回扣你最初的假设。

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8. Drawing Conclusions and Evaluating | 得出结论与评估

Your conclusion must directly answer the research question and state whether the hypothesis is supported. Avoid overgeneralising. For a sample of 18 Year 9 students you might write: ‘Within this sample, students who spent more time on mobile phones did sleep less on average, supporting the hypothesis. However, this conclusion applies only to the students studied and may not hold for all Year 9 students.’

你的结论必须直接回答研究问题，并说明假设是否得到支持。避免过度推论。对于 18 名九年级学生的样本，你可以写道：“在本样本中，手机使用时间较长的学生平均睡眠时间确实更少，这支持了假设。然而，该结论仅适用于所研究的学生，可能并不适用于所有九年级学生。”

Evaluation is critical for higher marks. Discuss limitations such as a small sample size, self-reported data (which may be inaccurate), and lack of control for other factors like screen brightness or caffeine intake. Suggest improvements, such as a larger sample across multiple schools or using digital tracking for more objective data.

评估对于获得高分至关重要。讨论一些局限性，比如样本量小、自我报告的数据（可能不准确），以及未能控制其他因素，例如屏幕亮度或咖啡因摄入。提出改进建议，比如扩大样本、覆盖多所学校，或使用数字追踪以获取更客观的数据。

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9. Formatting Your Report | 报告格式

Your final report should follow a standard academic structure. Use clear headings: Title, Introduction (including hypothesis), Method, Results (with tables and graphs), Analysis, Conclusion, and Evaluation. Number all tables and figures sequentially and refer to them in the text, e.g., ‘As shown in Table 1, the phone usage ranged from 2.0 to 7.5 hours.’

最终报告应遵循标准学术结构。使用清晰的标题：标题、引言（包括假设）、方法、结果（含表格和图）、分析、结论、评估。为所有表格和图按顺序编号，并在正文中引用，例如：“如表 1 所示，手机使用时间在 2.0 至 7.5 小时之间。”

Write in third person and past tense (e.g., ‘Data were collected’). Keep the language precise and avoid casual expressions. All calculations should be shown where appropriate, and units must be included throughout.

使用第三人称和过去时态（例如，“数据被收集”）。语言要准确，避免随意的表达。所有计算都应在适当位置展示，全文必须包含单位。

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10. Model Answer: Full Statistical Report | 范文：完整的统计报告

Title: Investigating the Relationship between Mobile Phone Use and Sleep Duration in Year 9 Students

标题：调查九年级学生手机使用与睡眠时长之间的关系

Abstract: This investigation explored whether Year 9 students who use mobile phones for longer each day tend to sleep fewer hours at night. A sample of 10 students was surveyed, recording typical daily phone use and average sleep duration. Analysis revealed a negative correlation: as phone use increased, sleep decreased. The mean sleep for low phone users was 8.2 hours, compared to 6.6 hours for high phone users, supporting the hypothesis.

摘要：本调查探讨了九年级学生是否每天使用手机时间越长，夜间睡眠时间越短。从 10 名学生中采集样本，记录其每日典型手机使用时间和平均睡眠时长。分析显示出负相关：随着手机使用时间的增加，睡眠时间减少。手机使用时间短的学生平均睡眠为 8.2 小时，而使用时间长的学生为 6.6 小时，这支持了假设。

Introduction: The aim was to answer ‘Is there a relationship between mobile phone usage and sleep among Year 9 students?’ It was hypothesised that higher phone usage is associated with lower sleep duration. This could have implications for student wellbeing.

引言：研究目的是回答“九年级学生的手机使用与睡眠之间是否存在关系？”假设较高的手机使用与较低的睡眠时长相关。这可能对学生的身心健康有所启示。

Method: A questionnaire was given to a convenience sample of 10 Year 9 students during a lunch break. They were asked to estimate their average daily phone use (in hours) and average nightly sleep (in hours) over the past week. All participants remained anonymous.

方法：在午休时间，向 10 名九年级学生组成的便利样本发放了问卷。他们被要求估计过去一周中平均每日手机使用时间（小时）和平均每晚睡眠时间（小时）。所有参与者均为匿名。

Results: Raw data are shown in Table 1.

结果：原始数据见表 1。

Student	Phone Use (hours)	Sleep (hours)
A	5.2	6.9
B	3.8	8.3
C	7.1	5.8
D	6.4	6.5
E	2.5	8.7
F	4.9	7.2
G	6.0	6.8
H	3.0	8.5
I	8.3	5.2
J	4.1	7.9

Table 1: Raw data of phone use and sleep for 10 students. The phone use values range from 2.5 to 8.3 hours, while sleep ranges from 5.2 to 8.7 hours.

表 1：10 名学生的手机使用与睡眠原始数据。手机使用值在 2.5 至 8.3 小时之间，而睡眠值在 5.2 至 8.7 小时之间。

A scatter graph was plotted with phone use on the horizontal axis and sleep on the vertical axis. The points showed a clear downward trend, indicating a negative correlation. A line of best fit was drawn to model the relationship.

然后绘制了散点图，横轴为手机使用时间，纵轴为睡眠时间。这些点呈现出明显的下降趋势，表明存在负相关。图中添加了最佳拟合线以呈现这种关系。

Summary statistics were calculated. For phone use: Mean = (5.2+3.8+7.1+6.4+2.5+4.9+6.0+3.0+8.3+4.1) ÷ 10 = 51.3 ÷ 10 = 5.13 hours. Median (ordered: 2.5, 3.0, 3.8, 4.1, 4.9, 5.2, 6.0, 6.4, 7.1, 8.3) = 5.05 hours. Range = 8.3 – 2.5 = 5.8 hours. For sleep: Mean = (6.9+8.3+5.8+6.5+8.7+7.2+6.8+8.5+5.2+7.9) ÷ 10 = 71.8 ÷ 10 = 7.18 hours. Median = 7.0 hours. Range = 8.7 – 5.2 = 3.5 hours.

还计算了汇总统计量。对于手机使用时间：平均值 = (5.2+3.8+7.1+6.4+2.5+4.9+6.0+3.0+8.3+4.1) ÷ 10 = 51.3 ÷ 10 = 5.13 小时。中位数（排序后：2.5, 3.0, 3.8, 4.1, 4.9, 5.2, 6.0, 6.4, 7.1, 8.3）= 5.05 小时。极差 = 8.3 – 2.5 = 5.8 小时。对于睡眠时间：平均值 = (6.9+8.3+5.8+6.5+8.7+7.2+6.8+8.5+5.2+7.9) ÷ 10 = 71.8 ÷ 10 = 7.18 小时。中位数 = 7.0 小时。极差 = 8.7 – 5.2 = 3.5 小时。

Analysis: The negative gradient of the scatter graph confirms that higher phone use tends to be linked with lower sleep. Comparing the top three phone users (Students C, I, D with phone use > 6.4 hours) to the bottom three (E, H, B with < 3.8 hours) reveals an average sleep of 5.83 hours versus 8.50 hours – a difference of 2.67 hours. This supports the hypothesis strongly.

分析：散点图的负斜率证实，较高的手机使用往往与较低的睡眠相关联。比较手机使用时间最多的三名学生（学生 C、I、D，手机使用 > 6.4 小时）和最少的三人（E、H、B，< 3.8 小时），其平均睡眠分别为 5.83 小时和 8.50 小时，相差 2.67 小时。这有力地支持了假设。

Conclusion: The data from this sample of Year 9 students

Published by TutorHao | Year 9 统计 Revision Series | aleveler.com

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