📚 Year 9 CIE Statistics: Unit Test Mock Paper Walkthrough | Year 9 CIE 统计：单元测试模拟卷解析
This article walks you through a typical Year 9 CIE Statistics unit test mock paper. For each question, we break down the key concepts, show the correct reasoning step by step, and highlight common pitfalls. Working through these solutions will strengthen your understanding of data collection, representation, averages, spread, and probability.
本文带你逐题解析一份典型的 Year 9 CIE 统计单元测试模拟卷。每道题我们都会拆解核心概念，逐步展示正确思路，并指出常见易错点。完成这些解析能帮你巩固数据收集、图表表达、平均数、离散程度和概率等知识。
1. Question 1: Data Classification | 第 1 题：数据分类
A survey records the following variables: favourite subject, number of books read this year, time taken to travel to school, and preferred learning style. Classify each item as categorical, discrete numerical, or continuous numerical.
一项调查记录了以下变量：最喜欢的科目、今年读过的书的数量、上学所用时间和偏好的学习方式。请将每一项分为分类数据、离散数值数据或连续数值数据。
Favourite subject is categorical because it describes a quality or category without a natural numeric order.
最喜欢的科目属于分类数据，因为它描述的是性质或类别，没有内在的数值顺序。
Number of books read is discrete numerical; it is obtained by counting and can only take whole numbers (e.g. 0, 1, 2, 3 …).
读过的书的数量是离散数值数据，通过计数得到，只能取整数（如 0、1、2、3……）。
Time taken to travel to school is continuous numerical; time can be measured to any level of precision and can take any value within a range.
上学所用时间是连续数值数据，时间可以测量到任意精度，可在一定范围内取任何值。
Preferred learning style is categorical, as it groups responses into named styles (visual, auditory, kinesthetic) without numerical meaning.
偏好的学习方式属于分类数据，它将回答归入不同的命名方式（视觉、听觉、动觉）且没有数值含义。
Always check whether a number is used as a label: if so, it is categorical data, not numerical.
始终检查数字是否仅作为标签使用：如果是，那就是分类数据，而非数值数据。
2. Question 2: Finding the Mean from a Frequency Table | 第 2 题：根据频率表求平均数
A class of 25 students recorded the number of siblings they have. The results are shown in the frequency table below. Calculate the mean number of siblings.
某班 25 名学生记录了他们拥有的兄弟姐妹人数，结果如下表所示。请计算平均兄弟姐妹人数。
| Number of siblings | 兄弟姐妹数 | Frequency | 频数 |
|---|---|
| 0 | 8 |
| 1 | 10 |
| 2 | 5 |
| 3 | 2 |
Multiply each number of siblings by its frequency: 0 × 8 = 0, 1 × 10 = 10, 2 × 5 = 10, 3 × 2 = 6. The total of these products is 0 + 10 + 10 + 6 = 26.
将每组兄弟姐妹数乘以对应频数：0 × 8 = 0，1 × 10 = 10，2 × 5 = 10，3 × 2 = 6。乘积总和为 0 + 10 + 10 + 6 = 26。
Divide the total (26) by the sum of frequencies (25) to obtain the mean: 26 ÷ 25 = 1.04 siblings.
用总和（26）除以总频数（25）得到平均数：26 ÷ 25 = 1.04 个兄弟姐妹。
Always check that you have multiplied all the data values by their correct frequencies before adding.
在相加之前，务必确认已将所有数据值与正确的频数相乘。
3. Question 3: Interpreting a Dual Bar Chart | 第 3 题：解读双条形图
A stationery shop recorded the sales of pens and pencils over four months. The dual bar chart below (data represented here numerically) shows the results. Use the data to state one comparison and one difference between the sales trends.
一家文具店记录了四个月内钢笔和铅笔的销售情况。下面的双条形图（此处用数字表示）显示了结果。请利用数据，说明销售趋势的一个共同点和一个不同点。
| Month | 月份 | Pens sold | 钢笔销量 | Pencils sold | 铅笔销量 |
|---|---|---|
| Jan | 45 | 60 |
| Feb | 55 | 70 |
| Mar | 40 | 55 |
| Apr | 50 | 65 |
Comparison: For every month, more pencils were sold than pens. The pencil sales are consistently higher.
共同点：每个月铅笔的销量都高于钢笔，铅笔销量始终更多。
Difference: The trend for pens shows a dip in March (from 55 to 40) before rising again, whereas pencil sales decrease gradually from February to March but do not show such a sharp drop.
不同点：钢笔销量在三月出现下降（从 55 降至 40）然后再次回升，而铅笔销量从二月到三月缓缓减少，但没有如此剧烈的下跌。
When analysing dual bar charts, always read the key to identify which bar represents which category, and look for patterns over time.
分析双条形图时，务必阅读图例以区分不同类别的条形，并寻找随时间变化的规律。
4. Question 4: Pie Chart Angles and Frequency | 第 4 题：饼图角度与频数
A survey of 180 people about their favourite fruit gave the following sector angles in a pie chart: Apple 120°, Banana 80°, Orange 60°, Grape 100°. Calculate the number of people who chose each fruit.
一项针对 180 人最喜欢水果的调查显示，饼图中各扇区角度为：苹果 120°，香蕉 80°，橙子 60°，葡萄 100°。计算选择每种水果的人数。
Recall that a full circle is 360°, representing all 180 people. So each degree represents 180 ÷ 360 = 0.5 people.
一个完整圆周为 360°，代表全部 180 人。因此每度代表 180 ÷ 360 = 0.5 人。
Apple: 120° × 0.5 = 60 people. Banana: 80° × 0.5 = 40 people. Orange: 60° × 0.5 = 30 people. Grape: 100° × 0.5 = 50 people. Check: 60 + 40 + 30 + 50 = 180, which matches the total.
苹果：120° × 0.5 = 60 人。香蕉：80° × 0.5 = 40 人。橙子：60° × 0.5 = 30 人。葡萄：100° × 0.5 = 50 人。验证：60 + 40 + 30 + 50 = 180，与总数一致。
A common mistake is forgetting to convert the total frequency to degrees correctly. Always set up the proportion: sector angle/360 = frequency/total frequency.
常见错误是忘记正确地将总频数转换为角度。一定要建立比例关系：扇区角度/360 = 频数/总频数。
5. Question 5: Median, Mode and Range | 第 5 题：中位数、众数和全距
The heights (in cm) of 11 basketball players are: 182, 190, 185, 188, 185, 192, 185, 183, 190, 187, 189. Find the mode, median, and range of this data set.
11 名篮球运动员的身高（单位：厘米）如下：182、190、185、188、185、192、185、183、190、187、189。求该数据集的众数、中位数和全距。
Mode is the most frequent value. Here, 185 appears three times, so mode = 185 cm.
众数是出现频率最高的值。本例中 185 出现三次，因此众数为 185 cm。
To find the median, arrange the data in ascending order: 182, 183, 185, 185, 185, 187, 188, 189, 190, 190, 192. With 11 values, the median is the 6th value, which is 187 cm.
求中位数时，将数据按升序排列：182，183，185，185，185，187，188，189，190，190，192。共 11 个值，中位数为第 6 个值，即 187 cm。
Range = Maximum – Minimum = 192 – 182 = 10 cm.
全距 = 最大值 – 最小值 = 192 – 182 = 10 cm。
For an odd number of data points, the median is the middle one; for an even number, it is the mean of the two middle values.
若数据点数为奇数，中位数即正中间的值；若为偶数，则为中间两个值的平均数。
6. Question 6: Probability from Sample Space | 第 6 题：根据样本空间求概率
A fair six-sided die is rolled and a fair coin is flipped. List the sample space for this experiment and find the probability of obtaining an even number on the die and a head on the coin.
同时掷一枚均匀六面骰子并抛一枚均匀硬币。列出该试验的样本空间，并求掷得骰子偶数和硬币正面的概率。
The sample space can be listed as (Die, Coin) pairs: (1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T). Total outcomes = 12.
样本空间可列出所有（骰子, 硬币）组合：(1,正), (1,反), (2,正), (2,反), (3,正), (3,反), (4,正), (4,反), (5,正), (5,反), (6,正), (6,反)。总结果数 = 12。
Favourable outcomes: even numbers are 2, 4, 6 with a head. These are (2,H), (4,H), (6,H). So 3 favourable outcomes.
有利结果：骰子偶数（2、4、6）且为正面。即 (2,H)，(4,H)，(6,H)。共 3 个有利结果。
Probability = 3/12 = 1/4 or 0.25.
概率 = 3/12 = 1/4 或 0.25。
Listing the sample space systematically ensures you don’t miss outcomes. Probability is always favorable outcomes divided by total possible outcomes.
系统性地列出样本空间可以确保不会遗漏结果。概率总是有利结果数除以所有可能结果数。
7. Question 7: Scatter Graphs and Correlation | 第 7 题：散点图与相关性
The table shows the number of hours ten students spent revising and their test scores. Draw a scatter graph and describe the type and strength of correlation shown.
下表显示了十名学生的复习小时数和测试成绩。绘制散点图并描述所示相关性的类型和强度。
| Revision hours | 复习小时数 | Test score (%) | 测试分数(%) |
|---|---|
| 0.5 | 30 |
| 1.0 | 40 |
| 1.5 | 45 |
| 2.0 | 55 |
| 2.5 | 65 |
| 3.0 | 70 |
| 3.5 | 72 |
| 4.0 | 80 |
| 4.5 | 85 |
| 5.0 | 95 |
When plotted, the points generally rise from bottom-left to top-right, indicating a positive correlation: as revision hours increase, test scores tend to increase.
将各点绘出后，大致从左下向右上延伸，表明正相关：随着复习时间增加，测验分数也趋向提高。
The points lie quite close to a straight line, so the correlation is strong. There are no obvious outliers.
这些点紧靠一条直线，所以相关性较强。无明显异常值。
In describing correlation, always mention its direction (positive, negative, or none) and strength (strong, moderate, weak).
描述相关性时，务必提到方向（正、负或无）和强度（强、中等、弱）。
8. Question 8: Stem-and-Leaf Diagram | 第 8 题：茎叶图
The stem-and-leaf diagram shows the ages of participants at a community event. Key: 3 | 2 means 32 years.
茎叶图显示了社区活动参与者的年龄。图例：3 | 2 代表 32 岁。
| Stem | 茎 | Leaf | 叶 |
|---|---|
| 2 | 8, 9 |
| 3 | 2, 4, 5, 5 |
| 4 | 0, 1, 3, 7 |
| 5 | 2, 5 |
List all the ages and find the median age.
列出所有年龄并求中位数年龄。
The ages are: 28, 29, 32, 34, 35, 35, 40, 41, 43, 47, 52, 55. There are 12 values in total. With an even number, the median is the mean of the 6th and 7th values in order: 6th = 35, 7th = 40, so median = (35 + 40) ÷ 2 = 37.5 years.
所有年龄为：28，29，32，34，35，35，40，41，43，47，52，55。总共 12 个值。偶数个时，中位数为排序后第 6 和第 7 个值的平均数：第 6 个为 35，第 7 个为 40，所以中位数 = (35 + 40) ÷ 2 = 37.5 岁。
In a stem-and-leaf diagram, the leaves must be arranged in increasing order away from the stem to make the median easy to locate.
在茎叶图中，叶必须按升序远离茎排列，以便于找到中位数。
9. Question 9: Misleading Graphs | 第 9 题：误导性图表
A newspaper bar chart claims that a cinema’s ticket sales have nearly tripled because last year’s bar is drawn at height 2 cm and this year’s bar at 6 cm. However, the vertical axis starts at 80 tickets, not zero. Explain why the graph is misleading and what the actual percentage increase is if last year’s sales were 82 and this year’s 86.
某报纸的条形图声称一家电影院的售票量几乎翻了三倍，因为去年的柱高为 2 厘米，今年的为 6 厘米。但纵轴起点为 80 张而非 0。请解释为什么此图具有误导性，并计算如果去年售票 82 张、今年 86 张，实际增长百分比是多少。
By starting the axis at 80, the visual difference between 82 and 86 is exaggerated. The bar heights (2 cm vs 6 cm) suggest a threefold increase, but the actual increase is only 4 tickets.
由于纵轴从 80 开始，82 与 86 之间的视觉差异被放大。柱高（2 厘米对 6 厘米）暗示增长了三倍，而实际只增加了 4 张票。
Actual percentage increase = (86 – 82) ÷ 82 × 100% ≈ 4.88%. The graph misleads the reader because a truncated axis distorts the scale.
实际增长百分比 = (86 – 82) ÷ 82 × 100% ≈ 4.88%。该图误导了读者，因为截断的坐标轴扭曲了比例。
Always check the vertical scale and whether it starts at zero when interpreting bar charts. A graph can be made misleading by stretching or compressing either axis.
解读条形图时，务必检查纵轴刻度以及是否从零开始。通过拉伸或压缩任一坐标轴，都可能使图表产生误导。
10. Question 10: Designing a Survey Question | 第 10 题：设计调查问题
A student wants to investigate how much time Year 9 learners spend on homework each evening. Design a suitable survey question, including three possible response options, and identify two factors that should be kept constant to make the data reliable.
一名学生想调查 Year 9 学生每晚花多少时间做作业。请设计一个合适的调查问题，包括三个可能的回答选项，并指出两个应保持固定以确保数据可靠的因素。
Suggested question: ‘On a typical school night, how long do you spend on homework? (a) Less than 30 minutes, (b) 30 to 60 minutes, (c) More than 60 minutes.’
建议的问题：“在通常的学习日晚上，你花多少时间做作业？(a) 少于 30 分钟，(b) 30 到 60 分钟，(c) 超过 60 分钟。”
Factors to keep constant: (1) The definition of ‘homework’ should be clear – e.g. set by teacher, not including revision by choice. (2) The data should be collected during the same time of the school term to avoid exam period bias.
应固定的因素：(1) 应明确“作业”的定义——例如，仅限老师布置的，不包括自主复习。(2) 数据应在学期内同一时段收集，以避免考试期造成的偏差。
A well-designed question avoids leading or vague wording. Response options should be exhaustive and mutually exclusive so every participant fits into exactly one category.
精心设计的问题应避免诱导性或模糊的措辞。回答选项应详尽且互斥，以便每位参与者恰好归入一个类别。
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