📚 Year 9 OCR Statistics: Unit Test Mock Paper Walkthrough | Year 9 OCR 统计：单元测试模拟卷解析
Welcome to the Year 9 OCR Statistics Unit Test Mock Paper Walkthrough. This article takes you through a full mock paper, question by question, highlighting key concepts, common mistakes, and the best ways to present your working. By the end, you will have a clearer idea of what examiners look for and how to structure your answers effectively.
欢迎来到Year 9 OCR统计单元测试模拟卷解析。本文将逐题讲解一套完整的模拟卷，突出关键概念、常见错误以及展示解题过程的最佳方式。读完后，你将更清楚考官看重什么，以及如何有效地组织你的答案。
1. Data Collection and Sampling | 数据收集与抽样
A mock question may ask: 'A fitness app wants to survey Year 9 pupils about their weekly exercise. There are 180 pupils in the year group. Suggest a sensible sample size and a method to select the sample without bias.' The population is the 180 Year 9 pupils. A sample size of 30 to 40 is reasonable; you could use a simple random sampling method. Assign each pupil a number from 1 to 180 and use a random number generator to pick your sample. This gives everyone an equal chance of being chosen, reducing bias.
模拟题可能会问：“某健身App想调查Year 9学生每周锻炼情况。年级共有180名学生。提出一个合理的样本容量以及无偏抽取样本的方法。”总体是这180名Year 9学生。样本容量在30至40之间是合理的；你可以采用简单随机抽样。给每名学生分配从1到180的编号，然后用随机数生成器选取样本。这使得每人被选中的机会均等，减少了偏差。
Avoid convenience sampling, such as only asking your friends, because that sample is unlikely to represent the whole year group. A census would ask everyone but is more time‑consuming, and in this context a well‑chosen sample is sufficient.
要避免便利抽样，例如只询问自己的朋友，因为这样的样本不太可能代表整个年级。普查会询问每一个人，但比较耗时，在这种情况下，一个精心选出的样本就足够了。
2. Designing a Questionnaire | 设计调查问卷
You might be asked to write one unbiased question about screen time. A good closed question would be: 'How many hours of recreational screen time do you have per day?' with non‑overlapping response boxes: 'Less than 1', '1–2', '2–3', '3–4', 'Over 4'. The categories are exhaustive and mutually exclusive, so every pupil can choose one option without confusion.
你可能会被要求写出一个关于屏幕时间的无偏问题。一个好的封闭式问题是：“你每天有多少小时的娱乐屏幕时间？”并设置不重叠的选项框：“少于1”、“1–2”、“2–3”、“3–4”、“超过4”。这些分类既穷尽又互斥，因此每个学生都能清楚地做出唯一选择。
Leading questions such as 'Don't you think too much screen time is bad?' should be avoided because they push respondents towards a particular answer. Pilot the question on a small group first to check that everyone interprets it in the same way.
应避免诱导性问题，如“你难道不认为过多的屏幕时间有害吗？”因为这类问题会把受访者推向某个特定答案。可先在一小群人中进行试调查，确保每个人对问题的理解相同。
3. Interpreting Bar Charts and Pie Charts | 解读条形图和饼图
Suppose a bar chart shows favourite snacks: Crisps 40, Chocolate 30, Fruit 15, Biscuits 25. From the bar chart, you can read frequencies directly. The total number of responses is 110. The proportion who chose fruit is 15/110, which simplifies to 3/22. The mode is crisps.
假设一个条形图显示了最受喜爱的零食：薯片40人，巧克力30人，水果15人，饼干25人。从条形图上你可以直接读取频数。总应答数是110。选择水果的比例是15/110，可化简为3/22。众数是薯片。
rt is useful for seeing proportions, but it is harder to compare exact frequencies than with a bar chart.
如果同样的数据用饼图展示，水果扇区的角度为(15/110) × 360° ≈ 49.1°。饼图适合观察比例，但相比条形图，较难比较精确的频数。
4. Calculating Mean, Median, Mode and Range | 计算平均数、中位数、众数和极差
e. The median is the average of the 4th and 5th values: (12+15)/2 = 13.5. The mode is 15, as it occurs most often. The range is 20 − 6 = 14.
考虑数据集：6, 10, 10, 12, 15, 15, 15, 20。平均数是(6+10+10+12+15+15+15+20) ÷ 8 = 108 ÷ 8 = 13.5。将数值排序（已有序）。中位数是第4和第5个值的平均数：(12+15)/2 = 13.5。众数是15，因为它出现的次数最多。极差为20 − 6 = 14。
Note that the mean can be pulled up or down by extreme values, while the median stays central. In this set, the mean and median are equal, suggesting a fairly symmetric distribution.
注意，平均数可能被极端值拉高或拉低，而中位数始终居中。在这个数据中，平均数与中位数相等，表明分布大致对称。
5. Finding Quartiles and Interquartile Range | 求四分位数和四分位距
15, 15, 20; its median is (15+15)/2 = 15, so Q₃ = 15. The interquartile range (IQR) = Q₃ − Q₁ = 15 − 10 = 5.
使用同样的有序数据集：6, 10, 10, 12, 15, 15, 15, 20。下半部分是6, 10, 10, 12；其中位数是(10+10)/2 = 10，所以Q₁ = 10。上半部分是15, 15, 15, 20；其中位数是(15+15)/2 = 15，所以Q₃ = 15。四分位距（IQR）= Q₃ − Q₁ = 15 − 10 = 5。
The IQR measures the spread of the middle 50% of the data. It is not affected by outliers, whereas the range is. You would use the IQR alongside the median when comparing sets with skewed distributions.
IQR衡量中间50%数据的离散程度。它不受异常值影响，而极差则会受影响。在比较偏态分布的数据集时，你应结合中位数和IQR来使用。
6. Drawing and Reading Stem-and-Leaf Diagrams | 绘制和解读茎叶图
A mock paper may give test scores: 62, 68, 71, 74, 75, 78, 83, 85, 88, 92. A stem‑and‑leaf diagram uses the tens as the stem and the units as leaves. For example, 6 | e median. With 10 values, the median is halfway between the 5th and 6th: (75+78)/2 = 76.5.
模拟卷可能给出测试分数：62, 68, 71, 74, 75, 78, 83, 85, 88, 92。茎叶图以十位数为茎，个位数为叶。例如，6 | 2 8 表示62和68。该图能让你轻松看出分布形状并找到中位数。有10个值时，中位数是第5和第6个值的中间值：(75+78)/2 = 76.5。
Always include a key, such as '6|2 means 62'. Stem‑and‑leaf diagrams retain the original data, unlike a bar chart, so you can still calculate the mean and range from the display.
务必加上图例，如“6|2表示62”。茎叶图保留了原始数据，而不像条形图那样，因此你仍然可以从这幅图计算平均数和极差。
7. Scatter Graphs and Correlation | 散点图与相关性
For a scatter graph of hours studied versus test marks, you plot each pupil as a point. If the points show an upward trend, there is a positive correlation: more study hours are linked to higher marks. A line of best fit can be drawn, passing through the middle of the points, roughly half above and half below.
对于学习时间与考试成绩的散点图，你把每个学生画为一个点。若这些点呈上升趋势，则存在正相关：更多的学习时间与更高的分数相关。可以画一条最佳拟合线，穿过这些点的中间，使其上方和下方的点大致各占一半。
Correlation does not mean one variable causes the other to change. Other factors, such as natural ability or quality of teaching, may also affect marks. When describing correlation, use terms like 'strong positive', 'weak negative' or 'no correlation'.
相关性并不意味着一个变量的变化会引发另一个变量的变化。其他因素，如天赋或教学质量，也可能影响分数。在描述相关性时，请使用“强正相关”、“弱负相关”或“无相关”等术语。
8. Basic Probability from Two-way Tables | 双向表格的基础概率
A two‑way table shows the number of boys and girls who prefer Science or Art. For example:
| Science | Art | Total | |
|---|---|---|---|
| Boys | 18 | 12 | 30 |
| Girls | 15 | 25 | 40 |
| Total | 33 | 37 | 70 |
a boy is 30/70 = 3/7. Always simplify your fractions unless the question states otherwise.
根据表格，随机选中的学生是一名喜欢艺术的女孩的概率是25/70 = 5/14。选中男孩的概率是30/70 = 3/7。除非题目另有要求，请始终将分数化简。
heck that probabilities sum correctly: P(Science) + P(Art) = 33/70 + 37/70 = 1. This total‑probability check helps avoid careless errors.
检查概率之和是否正确：P(科学) + P(艺术) = 33/70 + 37/70 = 1。这一总概率检查有助于避免粗心错误。
9. Expected Frequency and Relative Frequency | 期望频数与相对频率
. The expected frequency is what theory predicts, whereas the actual or observed frequency comes from an experiment. The relative frequency after,
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