📚 KS3 CIE Statistics: Unit Test Mock Paper Analysis | KS3 CIE 统计：单元测试模拟卷解析
This article presents a complete unit test mock paper covering the essential topics in KS3 CIE Statistics, from averages and charts to probability and data analysis. Each question is followed by a detailed step-by-step solution, common pitfalls, and key takeaways to support effective revision.
本文提供一套涵盖 KS3 CIE 统计学核心内容的单元测试模拟卷，涉及平均数、统计图表、概率及数据分析等重点知识。每道题目均配有详细的分步解析、常见错误提醒和解题要点，帮助同学们高效复习。
1. Mean, Median, Mode and Range | 平均数、中位数、众数与极差
The number of goals scored by a football team in 10 matches is: 2, 1, 3, 0, 2, 2, 4, 1, 3, 2. Find the mean, median, mode and range.
一支足球队在 10 场比赛中的进球数为：2, 1, 3, 0, 2, 2, 4, 1, 3, 2。计算这组数据的平均数、中位数、众数和极差。
To find the mean, add all values: 2+1+3+0+2+2+4+1+3+2 = 20. Divide by the number of matches (10): 20 ÷ 10 = 2. Mean = 2 goals.
计算平均数：先求和 2+1+3+0+2+2+4+1+3+2 = 20，再除以比赛场次 10，得到 20 ÷ 10 = 2。平均数为 2 球。
For the median, arrange the numbers in ascending order: 0, 1, 1, 2, 2, 2, 2, 3, 3, 4. Since there are 10 values (even), the median is the average of the 5th and 6th values: (2+2)/2 = 2. Median = 2 goals.
求中位数：将数据升序排列为 0, 1, 1, 2, 2, 2, 2, 3, 3, 4。共 10 个数据（偶数），中位数为第 5 个与第 6 个数的平均值：(2+2)/2 = 2。中位数为 2 球。
The mode is the value that appears most often. The number 2 appears four times, more than any other value. Mode = 2 goals.
众数是出现次数最多的值。数字 2 出现了 4 次，多于其他任何数字，众数为 2 球。
The range is the difference between the largest and smallest values: 4 – 0 = 4. Range = 4 goals.
极差等于最大值减最小值：4 – 0 = 4。极差为 4 球。
2. Bar Chart Interpretation | 条形图解读
A bar chart shows the number of ice creams sold at a shop from Monday to Sunday. The frequencies are: Monday 30, Tuesday 45, Wednesday 50, Thursday 40, Friday 65, Saturday 80, Sunday 70.
某商店一周（周一至周日）冰淇淋销量条形图显示如下数据：周一 30，周二 45，周三 50，周四 40，周五 65，周六 80，周日 70。
Which day had the highest sales? Saturday recorded the highest sales with 80 ice creams.
哪一天的销量最高？周六销量最高，为 80 个冰淇淋。
How many more ice creams were sold on Friday than on Thursday? Friday 65 minus Thursday 40 = 25 more ice creams.
周五比周四多卖出多少个冰淇淋？周五 65 个减去周四 40 个，多卖出 25 个。
Calculate the total number of ice creams sold during the week. Total = 30+45+50+40+65+80+70 = 380 ice creams.
计算一周的总销量。总和 = 30+45+50+40+65+80+70 = 380 个冰淇淋。
Find the mean number of ice creams sold per day. Mean = 380 ÷ 7 ≈ 54.3 ice creams per day (to 1 decimal place).
求每天的平均销量。平均数 = 380 ÷ 7 ≈ 54.3 个/天（保留一位小数）。
3. Pie Chart and Percentages | 饼图与百分比
A school surveyed 800 students about their favourite subject. The results: Maths 30%, Science 25%, English 20%, History 15%, Other 10%.
一所学校调查了 800 名学生最喜欢的科目，结果如下：数学 30%，科学 25%，英语 20%，历史 15%，其他 10%。
How many students chose Maths? 30% of 800 = (30/100) × 800 = 240 students.
选择数学的学生有多少人？800 的 30% = (30/100) × 800 = 240 人。
What fraction of students preferred English? 20% as a simplified fraction is 20/100 = 1/5.
喜欢英语的学生占几分之几？20% 转化为最简分数为 20/100 = 1/5。
How many students chose History? 15% of 800 = 0.15 × 800 = 120 students.
选择历史的学生有多少人？800 的 15% = 0.15 × 800 = 120 人。
Verify the remaining number for ‘Other’: 10% of 800 = 80 students. Total: 240+200+160+120+80 = 800, correct.
验证“其他”类别的学生数：800 的 10% = 80 人。总和 240+200+160+120+80 = 800，正确无误。
4. Stem-and-Leaf Plot | 茎叶图
A stem-and-leaf plot displays the scores of 12 students in a spelling test: Stem 1 | Leaf 2 5 8 (12, 15, 18); Stem 2 | Leaf 0 1 3 3 7 (20, 21, 23, 23, 27); Stem 3 | Leaf 0 4 6 (30, 34, 36); Stem 4 | Leaf 1 (41). Key: 1|2 means 12.
某拼写测试成绩的茎叶图如下：茎 1 | 叶 2 5 8（表示 12, 15, 18）；茎 2 | 叶 0 1 3 3 7（20, 21, 23, 23, 27）；茎 3 | 叶 0 4 6（30, 34, 36）；茎 4 | 叶 1（41）。图例：1|2 表示 12。
How many data values are there? Count all leaves: 3 (stem 1) + 5 (stem 2) + 3 (stem 3) + 1 (stem 4) = 12 values.
共有多少个数据？统计所有叶子数量：茎 1 有 3 个，茎 2 有 5 个，茎 3 有 3 个，茎 4 有 1 个，合计 12 个。
Find the median. With 12 values, the median lies between the 6th and 7th values. Ordered list: 12,15,18,20,21,23,23,27,30,34,36,41. The 6th is 23, 7th is 23, so median = 23.
求中位数。12 个数据的中位数是第 6 和第 7 个值的平均数。排序后为 12,15,18,20,21,23,23,27,30,34,36,41。第 6 和第 7 个值均为 23，中位数为 23。
Determine the range: maximum 41 – minimum 12 = 29.
求极差：最大值 41 减去最小值 12，等于 29。
Is there a mode? The value 23 appears twice; all others appear once. So the mode is 23.
众数是多少？数值 23 出现了两次，其他数值均只出现一次，因此众数为 23。
5. Probability from a Dice Roll | 掷骰子的概率
A fair six-sided die is rolled once. The faces are numbered 1, 2, 3, 4, 5, 6. Find the probability of: a) rolling an even number, b) rolling a number greater than 4, c) rolling a prime number.
抛掷一枚质地均匀的六面骰子一次，骰子面上的数字为 1、2、3、4、5、6。求以下事件的概率：a) 抛出偶数；b) 抛出大于 4 的数；c) 抛出质数。
Sample space = {1,2,3,4,5,6}, total outcomes = 6.
样本空间为 {1,2,3,4,5,6}，总共有 6 种等可能结果。
Even numbers are {2,4,6}. So P(even) = 3/6 = 1/2.
偶数为 {2,4,6}，共 3 种。因此 P(偶数) = 3/6 = 1/2。
Numbers greater than 4 are {5,6}. So P(>4) = 2/6 = 1/3.
大于 4 的数字为 {5,6}，共 2 种。P(大于 4) = 2/6 = 1/3。
Prime numbers on the die are {2,3,5}. (Note: 1 is not prime.) So P(prime) = 3/6 = 1/2.
骰面上的质数有 {2,3,5}（注意 1 不是质数）。因此 P(质数) = 3/6 = 1/2。
6. Scatter Graphs and Correlation | 散点图与相关性
The table below shows the Mathematics and Science test scores (out of 100) for eight students.
| Student | Maths | Science |
| A | 72 | 75 |
| B | 80 | 82 |
| C | 65 | 68 |
| D | 90 | 88 |
| E | 78 | 80 |
| F | 85 | 84 |
| G | 70 | 72 |
| H | 76 | 78 |
Display the data on a scatter graph and describe the correlation. Use the scatter graph to estimate the Science score for a student who scored 85 in Maths.
将数据绘制成散点图，并描述相关性。利用散点图估算数学成绩为 85 分的学生其科学成绩大约是多少。
When plotting, each pair (Maths, Science) forms a point. The points show a pattern: as Maths scores increase, Science scores also tend to increase. This indicates a positive correlation.
绘图时，每个学生的 (数学, 科学) 分数构成一个点。这些点呈现一种模式：随着数学分数增加，科学分数也趋于增加。这表明两者呈正相关。
The correlation is strong positive because the points lie close to a straight line sloping upwards.
相关性强且为正值，因为数据点紧密地分布在一根向上倾斜的直线周围。
To estimate for Maths 85, draw a line of best fit through the points. Extend the line to x = 85; read the y-value. It is approximately 84. So a student with Maths 85 would likely score around 84 in Science.
对于数学 85 分的估计，需要通过数据点画出最佳拟合线。将该线延伸到 x=85 处，读取对应的 y 值，大约为 84。因此数学 85 分的学生科学成绩很可能在 84 分左右。
7. Mean from a Frequency Table |
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