📚 Year 8 CIE Statistics Mock Test Walkthrough | Year 8 CIE 统计：单元测试模拟卷解析
This article provides a full walkthrough of a typical Year 8 CIE Statistics unit test. You will see mock questions covering tally charts, bar charts, measures of central tendency, pie charts, stem-and-leaf diagrams, scatter graphs and two-way tables. Every solution is explained step by step so you can understand exactly how marks are awarded and how to avoid common errors.
本文完整解析一份典型的 Year 8 CIE 统计单元测试模拟卷。你将看到涵盖计数符号表、条形图、集中趋势度量、饼图、茎叶图、散点图和双向表的模拟题。每道题的解答都分步讲解，让你清楚了解得分点的设置以及如何避免常见错误。
1. Question 1: Tally Charts and Frequency Tables | 第1题：计数符号与频数表
Question 1 (5 marks): A survey asked 20 students about their favourite fruit. The results are: apple, banana, apple, orange, banana, apple, grape, banana, apple, orange, apple, banana, grape, apple, orange, banana, apple, banana, orange, grape. (a) Complete the tally chart and frequency table. (b) Which fruit is the mode? (c) How many students chose orange or grape?
第1题（5分）：一项调查询问了20名学生最喜欢的水果。结果如下：苹果、香蕉、苹果、橙子、香蕉、苹果、葡萄、香蕉、苹果、橙子、苹果、香蕉、葡萄、苹果、橙子、香蕉、苹果、香蕉、橙子、葡萄。(a) 完成计数符号表和频数表。(b) 哪种水果是众数？(c) 有多少名学生选择了橙子或葡萄？
We need to count how many times each fruit appears. Go through the list one by one and draw a tally for each fruit. Every fifth tally should be drawn diagonally across the previous four to make groups of five easy to count.
我们需要统计每种水果出现的次数。逐个浏览列表，为每种水果画计数符号。每画到第五个符号时，应该斜穿前四个，这样一组五个便于点数。
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | IIII III | 8 |
| Banana | IIII I | 6 |
| Orange | IIII | 4 |
| Grape | II | 2 |
From the table, ‘apple’ has the highest frequency (8). So the mode is apple.
从表中可见，“苹果”出现的频率最高（8）。所以众数是苹果。
For part (c), add the frequency of orange (4) and grape (2): 4 + 2 = 6 students chose orange or grape.
对于(c)部分，将橙子的频数（4）和葡萄的频数（2）相加：4 + 2 = 6名学生选择了橙子或葡萄。
2. Question 2: Pictograms and Bar Charts | 第2题：象形图和条形图
Question 2 (4 marks): The frequency table shows the number of books read by Year 8 students in a month:
| Number of books | Frequency |
|---|---|
| 0 | 5 |
| 1 | 8 |
| 2 | 7 |
| 3 | 4 |
(a) Draw a pictogram where one book symbol represents 2 students. Show half symbols where needed. (b) Draw a vertical bar chart for the same data. Remember to label your axes and give the chart a title.
第2题（4分）：频数表显示了Year 8学生在一个月内阅读的书籍数量。 (a) 绘制一个象形图，其中一个书本符号代表2名学生。需要时使用半个符号。 (b) 为同一数据绘制一个垂直条形图。记得给坐标轴加标签并为图表加上标题。
For the pictogram, we divide each frequency by 2 because one symbol stands for 2 students. 5 students will be represented by 2.5 symbols, so draw two full book symbols and one half book symbol.
对于象形图，我们将每个频数除以2，因为一个符号代表2名学生。5名学生对应2.5个符号，所以画出两个完整的书本符号和一个半本书符号。
8 students = 4 full symbols, 7 students = 3.5 symbols (three full, one half), and 4 students = 2 full symbols. Always include a key, e.g. [book symbol] = 2 students.
8名学生 = 4个完整符号，7名学生 = 3.5个符号（三个完整、一个半），4名学生 = 2个完整符号。务必包含图例，例如[书本符号] = 2名学生。
When drawing the bar chart, use a uniform scale on the vertical axis. Label the horizontal axis ‘Number of books’ and the vertical axis ‘Frequency’. Every bar must be the same width and clearly spaced. Add a title like ‘Books read by Year 8 students in a month’.
绘制条形图时，纵轴使用均匀的刻度。横轴标注“书籍数量”，纵轴标注“频数”。每个条形的宽度必须一致且间距清晰。添加标题，如“Year 8学生一个月内阅读的书籍数量”。
3. Question 3: Mean, Median, Mode and Range | 第3题：平均数、中位数、众数和极差
Question 3 (6 marks): The following data set shows the marks of 10 students in a quiz: 12, 15, 18, 21, 15, 14, 15, 19, 20, 15. (a) Find the mode. (b) Calculate the mean, giving your answer to one decimal place. (c) Find the median. (d) Work out the range.
第3题（6分）：以下数据集显示了10名学生在一次测验中的分数：12, 15, 18, 21, 15, 14, 15, 19, 20, 15。 (a) 找出众数。 (b) 计算平均数，答案保留一位小数。 (c) 求中位数。 (d) 计算极差。
The mode is the value that appears most frequently. The number 15 appears four times, more than any other value, so mode = 15.
众数是出现次数最多的值。数字15出现了四次，比其他任何值都多，所以众数 = 15。
To calculate the mean, add all the values: 12 + 15 + 18 + 21 + 15 + 14 + 15 + 19 + 20 + 15 = 164. Divide by the number of students (10): 164 ÷ 10 = 16.4. So the mean is 16.4.
要计算平均数，先将所有值相加：12 + 15 + 18 + 21 + 15 + 14 + 15 + 19 + 20 + 15 = 164。然后除以学生人数（10）：164 ÷ 10 = 16.4。所以平均数是16.4。
For the median, first arrange the data in ascending order: 12, 14, 15, 15, 15, 15, 18, 19, 20, 21. Since there are 10 values (an even number), the median is the average of the 5th and 6th values. Both are 15, so (15 + 15) ÷ 2 = 15. The median is 15.
求中位数时，先将数据按升序排列：12, 14, 15, 15, 15, 15, 18, 19, 20, 21。因为有10个值（偶数个），中位数是第5和第6个值的平均数。两个值都是15，所以 (15 + 15) ÷ 2 = 15。中位数是15。
The range is the difference between the largest and smallest values: 21 – 12 = 9.
极差是最大值与最小值的差：21 – 12 = 9。
4. Question 4: Pie Charts and Angle Calculations | 第4题：饼图与角度计算
Question 4 (6 marks): A school club spends its monthly budget in the following way: Sports 40%, Arts 25%, Equipment 20%, Refreshments 15%. (a) Calculate the angle for each sector of a pie chart. (b) Draw the pie chart, labelling each sector clearly.
第4题（6分）：一个学校社团的月度预算分配如下：体育40%，艺术25%，设备20%，茶点15%。 (a) 计算饼图中每个扇区的角度。 (b) 绘制饼图，并清晰地给每个扇区标注。
The total angle in a pie chart is 360°. To find each sector angle, multiply the percentage by 360° and divide by 100 (or simply multiply the decimal form by 360°).
饼图的总角度是360°。求每个扇区角度时，将百分比乘以360°再除以100（或者直接将小数形式乘以360°）。
Sports: 40% of 360° = 0.4 × 360° = 144°. Arts: 25% of 360° = 0.25 × 360° = 90°. Equipment: 20% of 360° = 0.2 × 360° = 72°. Refreshments: 15% of 360° = 0.15 × 360° = 54°.
体育：360°的40% = 0.4 × 360° = 144°。艺术：0.25 × 360° = 90°。设备：0.2 × 360° = 72°。茶点：0.15 × 360° = 54°。
Check that the angles sum to 360°: 144° + 90° + 72° + 54° = 360°, which is correct. When drawing, start with a circle and use a protractor to measure each angle from the same radius. Label each sector with the category and its percentage.
检查各角度总和：144° + 90° + 72° + 54° = 360°，结果无误。绘制时先画一个圆，用量角器从同一条半径开始测量每个角度。每个扇区标注类别和百分比。
5. Question 5: Stem-and-Leaf Diagrams | 第5题：茎叶图
Question 5 (5 marks): The heights (in cm) of 12 plants are recorded: 43, 45, 48, 51, 52, 52, 53, 55, 58, 61, 63, 65. (a) Construct an ordered stem-and-leaf diagram. (b) Find the median height. (c) What is the range?
第5题（5分）：记录了12株植物的高度（单位cm）：43, 45, 48, 51, 52, 52, 53, 55, 58, 61, 63, 65。 (a) 构建一个有序的茎叶图。 (b) 求高度的中位数。 (c) 极差是多少？
In a stem-and-leaf diagram, the stem represents the tens digit and the leaf represents the units digit. For these data, stems will be 4, 5 and 6. Arrange leaves in ascending order.
在茎叶图中，茎代表十位数，叶代表个位数。对于这组数据，茎为4、5和6。将叶按升序排列。
Stem 4: leaves 3, 5, 8 (representing 43, 45, 48). Stem 5: leaves 1, 2, 2, 3, 5, 8 (51, 52, 52, 53, 55, 58). Stem 6: leaves 1, 3, 5 (61, 63, 65). Always include a key: 4|3 means 43 cm.
茎4：叶3, 5, 8（代表43, 45, 48）。茎5：叶1, 2, 2, 3, 5, 8（51, 52, 52, 53, 55, 58）。茎6：叶1, 3, 5（61, 63, 65）。务必附上图例：4|3 表示43 cm。
To find the median, list all values in order from the stem-and-leaf: 43, 45, 48, 51, 52, 52, 53, 55, 58, 61, 63, 65. With 12 values, the median is the average of the 6th and 7th values: (52 + 53) ÷ 2 = 52.5 cm.
为求中位数，从茎叶图中按顺序列出所有值：43, 45, 48, 51, 52, 52, 53, 55, 58, 61, 63, 65。有12个数据，中位数是第6和第7个值的平均数：(52 + 53) ÷ 2 = 52.5 cm。
Range = 65 – 43 = 22 cm.
极差 = 65 – 43 = 22 cm。
6. Question 6: Scatter Graphs and Correlation | 第6题：散点图与相关性
Question 6 (5 marks): A teacher records the number of hours spent revising and the test score out of 50 for 8 students. Hours: 2, 3, 5, 1, 8, 6, 4, 7. Scores: 20, 25, 35, 15, 45, 40, 30, 42. (a) Plot the data on a scatter graph. (b) Describe the correlation. (c) Estimate the test score for a student who revised for 5.5 hours.
第6题（5分）：一位老师记录了8名学生复习的小时数和满分50分的测验成绩。小时数：2, 3, 5, 1, 8, 6, 4, 7。成绩：20, 25, 35, 15, 45, 40, 30, 42。 (a) 将数据绘制在散点图上。 (b) 描述相关性。 (c) 估算复习了5.5小时的学生的测验成绩。
Plot each pair (hours, score) as a point. The axes should be labelled ‘Hours spent revising’ on the x-axis and ‘Test score’ on the y-axis. Choose a sensible scale.
将每一对（小时数，成绩）绘制为一个点。横轴标注“复习小时数”，纵轴标注“测验成绩”。选择合适的刻度。
Looking at the plotted points, as the number of hours increases, the test score also increases. The points roughly follow an upward trend, so this is a positive correlation.
观察点图，随着小时数增加，测验成绩也提高。这些点大致呈上升趋势，因此是正相关。
To estimate the score for 5.5 hours, draw a line of best fit through the points (not necessarily through the origin). From 5.5 on the x-axis, go up to the line and read the corresponding score value on the y-axis. This gives approximately 36 out of 50.
要估算5.5小时的成绩，在各点之间画一条最佳拟合线（不一定过原点）。从横轴上5.5处向上引到该线，再读取纵轴上对应的分数值。大约是50分中的36分。
7. Question 7: Interpreting Statistical Graphs | 第7题：统计图表的解读
Question 7 (5 marks): The bar chart below shows the number of ice creams sold each day from Monday to Friday. (Imagine the bar heights: Mon 15, Tue 12, Wed 18, Thu 20, Fri 25). (a) On which day were the fewest ice creams sold? (b) How many more ice creams were sold on Friday than on Monday? (c) What is the total number of ice creams sold over the five days? (d) Represent the Friday sales as a fraction of the total sales, in its simplest form.
第7题（5分）：下面的条形图显示了周一到周五每天售出的冰淇淋数量。（假设条形高度：周一15，周二12，周三18，周四20，周五25）。 (a) 哪天售出的冰淇淋最少？ (b) 周五比周一多卖出多少冰淇淋？ (c) 这五天售出的冰淇淋总数是多少？ (d) 用最简分数表示周五销量占总销量的比例。
The shortest bar is on Tuesday with 12 ice creams, so Tuesday had the fewest sales.
最短的条形在周二，为12个冰淇淋，所以周二销量最少。
Friday sales are 25, Monday sales are 15. Difference = 25 – 15 = 10 ice creams.
周五销量25，周一销量15。相差 = 25 – 15 = 10 个冰淇淋。
Total sales = 15 + 12 + 18 + 20 + 25 = 90 ice creams.
总销量 = 15 + 12 + 18 + 20 + 25 = 90 个冰淇淋。
Friday’s sales as a fraction of total = 25/90. Divide numerator and denominator by 5 to simplify: 25 ÷ 5 = 5, 90 ÷ 5 = 18, so the fraction is 5/18.
周五销量占总销量的比例 = 25/90。分子分母同时除以5来化简：25 ÷ 5 = 5，90 ÷ 5 = 18，所以分数是 5/18。
8. Question 8: Two-way Tables and Basic Probability | 第8题：双向表与基础概率
Question 8 (4 marks): The two-way table shows the number of boys and girls in Year 8 who walk or cycle to school.
| Walk | Cycle | Total | |
|---|---|---|---|
| Boys | 14 | 10 | 24 |
| Girls | 16 | 8 | 24 |
| Total | 30 | 18 | 48 |
(a) How many students cycle to school? (b) What is the probability that a randomly chosen student is a girl who walks? (c) A student is selected. Given that the student cycles, what is the probability the student is a boy?
第8题（4分）：双向表显示了Year 8步行或骑车上学的男生和女生数量。 (a) 有多少名学生骑车上学？ (b) 随机选择一名学生，她是步行上学的女生的概率是多少？ (c) 选出一名学生，已知该学生骑车，那么这名学生是男生的概率是多少？
Total cycling = 18 (from the table).
骑车总数 = 18（查表可得）。
Probability (girl and walks) = number of girls who walk / total students = 16/48. Simplify by dividing by 16: 1/3.
概率（步行女生）= 步行女生人数 / 学生总数 = 16/48。分子分母同除以16，得 1/3。
Given that the student cycles, we look only at the cycling column. Number of boys who cycle = 10. Total cycling = 18. Probability = 10/18 = 5/9 (simplified by dividing by 2).
已知该学生骑车，我们只看“骑车”这一列。骑车的男生数 = 10，骑车总人数 = 18。概率 = 10/18 = 5/9（分子分母同除以2）。
9. Tips for the Year 8 Statistics Mock Test | Year 8 统计模拟测试的答题技巧
Always show your working clearly. Even if your final answer is wrong, you can still earn method marks for a correct tally, ordered list, or division setup.
务必清晰地展示你的解题过程。即使最终答案错误，你仍可能因正确的计数符号、排序列表或除法算式而获得步骤分。
When drawing charts, use a sharp pencil and a ruler. Label axes, include a title, and make sure your scale is consistent. For pie charts, double-check that all angles sum to 360°.
绘制图表时，使用削尖的铅笔和直尺。标注坐标轴、给出标题，并确保刻度均匀。对于饼图，要再次确认所有角度之和为360°。
Read questions carefully to identify key phrases like ‘estimate’, ‘simplify’, ‘to one decimal place’, and ‘mode’. These specific instructions guide how you should present your final answer.
仔细读题，找出关键短语，如“估算”、“化简”、“保留一位小数”和“众数”。这些具体要求指引着你如何呈现最终答案。
Check your data ordering before finding the median. A single misplaced number will change the median and cause a mistake. For an even number of values, remember to average the two middle numbers.
在求中位数之前检查数据的排序。一个数字放错位置就会改变中位数，导致错误。对于偶数个数据，记住要取中间两个数的平均值。
10. Common Mistakes to Avoid | 需要避免的常见错误
Mistake
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