📚 Unit 5 S1 June 2019 Mark Scheme: High-Scoring Tips | 单元5 统计1 2019年6月评分方案高分技巧
Reviewing the June 2019 mark scheme for AS Mathematics Unit 5 (Statistics 1) reveals where candidates gained easy marks and where they lost them. This article distills the examiner’s comments into practical, high-scoring strategies that you can apply immediately, covering probability, correlation, normal distribution, and common pitfalls with data handling.
回顾2019年6月AS数学单元5（统计1）的评分方案，可以清楚看到考生在哪里轻松拿分，又在哪里频频失分。本文将考官评语提炼成可直接运用的高分策略，涵盖概率、相关性、正态分布以及数据处理中常见的陷阱。
1. State Assumptions for Full Marks on Probability Models | 写出概率模型的假设以拿满分
In the June 2019 Unit 5 paper, questions involving binomial or discrete uniform distributions often required a clear statement of assumptions. For a binomial model, writing “each trial is independent” and “the probability of success is constant” secures the final accuracy mark. Many candidates missed this by simply writing “it is binomial” without justification.
在2019年6月单元5的试卷中，涉及二项分布或离散均匀分布的问题常常要求明确写出假设。对于二项模型，写出“每次试验相互独立”和“成功概率恒定”就能拿下最后的准确度分。许多考生只是因为写了“这是二项分布”而未做解释，白白丢分。
- English: Always link the context to the assumption – e.g., “each student chosen independently” instead of generic “independent trials.”
- 中文：一定要将假设与情境联系起来——例如“每位学生被选中是相互独立的”，而不是泛泛地写“独立试验”。
The mark scheme shows that a minimal but contextualised sentence is enough to earn the mark. Practise writing these assumptions for past paper models until it becomes automatic.
评分方案表明，一句简短但与情境相关的句子就足以得分。请针对历年真题中的模型反复练习书写这些假设，直到形成条件反射。
2. Show All Possible Outcomes in Probability Calculations | 概率计算中展示所有可能结果
Examiners consistently award method marks for listing sample spaces or outcomes. In the June 2019 scheme, a question about the sum of two dice explicitly rewarded candidates who wrote down combinations like (1,3) and (2,2) for a sum of 4. Those who jumped directly to the probability without listing often lost the method mark, even if the final answer was correct.
考官会一贯地为列出样本空间或结果的方法打分。在2019年6月的评分方案中，一道关于两个骰子和的问题明确奖励了写出和为4的组合如(1,3)和(2,2)的考生。那些没有列表直接跳到概率的考生往往丢掉了方法分，即便最终答案正确。
P(Sum = 4) = P(1,3) + P(2,2) + P(3,1) = 3/36
Use a systematic approach: for two dice, create a quick grid or list. This not only earns you the method mark but also reduces careless errors with repeated pairs.
采用系统方法：对于两个骰子，快速画一个表格或列表。这样不仅能拿到方法分，还能减少因重复组合导致的粗心错误。
3. Master Conditional Probability from Tree Diagrams | 精通树形图中的条件概率
The June 2019 mark scheme placed heavy emphasis on conditional probability, with many marks allocated for correctly identifying P(A|B) from a tree diagram. A common error was confusing P(B|A) with P(A∩B). The scheme awarded one mark for writing the correct formula: P(A|B) = P(A∩B) / P(B).
2019年6月的评分方案对条件概率着重考察，大量分数分配给从树形图中正确识别P(A|B)。常见错误是把P(B|A)与P(A∩B)搞混。评分方案给写出正确公式P(A|B) = P(A∩B) / P(B)的考生1分。
To avoid this, label every branch with both the event and its probability. Whenever you see a “given that” phrase, redraw the relevant part of the tree and mark the restricted sample space.
避免这种错误的方法是为每条分支标出事件及其概率。每当你看到“已知……”的表述时，重新画出树形图的相关部分，并标明缩小的样本空间。
4. Tabulate Discrete Random Variables to Secure All Marks | 用表格表示离散随机变量以锁定全部分数
A question on a discrete random variable in the 2019 paper required candidates to find the probability distribution of a transformed variable. The mark scheme awarded one mark for listing all possible values of X, one mark for the corresponding transformed values, and a final mark for the probabilities summing to 1. Those who tried to work entirely in their heads frequently missed values or made arithmetic slips.
2019年试卷中一道关于离散随机变量的题目要求考生找出变换后变量的概率分布。评分方案针对列出X 所有可能值给1分，针对相应变换后的值给1分，最后针对概率和为1给1分。那些完全心算的考生经常遗漏数值或发生计算错误。
Create a neat table with columns: x, P(X=x), and the new variable y = g(x). The table makes it obvious whether probabilities sum to 1 and allows you to check each step. In the June 2019 scheme, even a partially correct table earned method marks.
制作一个清晰的表格，包括列：x、P(X=x)以及新变量y = g(x)。表格能够明确显示概率之和是否为1，并让你可以逐步检查。在2019年6月的评分方案中，即便是部分正确的表格也能拿到方法分。
5. Interpret Correlation with Both Strength and Direction | 解释相关性要同时提到强度与方向
The Unit 5 June 2019 paper included a scatter diagram and required an interpretation of the product moment correlation coefficient. The mark scheme demanded “positive correlation” and a comment on strength, such as “moderate” or “strong.” Single-word answers like “positive” received no marks; a full contextual phrase like “there is a moderate positive correlation between temperature and sales” was required.
单元5 2019年6月试卷中有一道散点图题目，要求解释积矩相关系数。评分方案要求给出“正相关”以及对强度的评论，如“中等”或“强”。单写“正”的答案不得分；需要完整的语境表述，例如“温度与销量之间存在中等正相关”。
Always write your interpretation in the context of the variables given. The 2019 mark scheme also awarded a mark for mentioning that correlation does not imply causation. Prepare a template: “There is [strength] [positive/negative] correlation between [variable1] and [variable2].”
务必根据给定的变量情境来写解释。2019年评分方案还奖励了提到相关不意味着因果的考生。请准备一个模板：“在[变量1]与[变量2]之间存在[强度][正/负]相关。”
6. Carry Extra Decimal Places in Regression Calculations | 回归计算时多保留几位小数
When calculating the equation of a regression line, the June 2019 mark scheme was strict about premature rounding. Candidates who rounded b (the gradient) to 3 significant figures before calculating a (the intercept) often produced an a value outside the acceptable range. The scheme allowed b = 0.516 (from b = 0.5157…) but penalised using b = 0.52.
在计算回归直线方程时，2019年6月的评分方案对过早四舍五入要求严格。那些在计算a（截距）之前就将b（斜率）取为3位有效数字的考生，经常得出超出可接受范围的a值。方案允许b = 0.516（来自b = 0.5157…），但惩罚使用b = 0.52的情况。
Keep b in calculator memory and use the stored value for a = ȳ − b x̄
Store intermediate values in your calculator without rounding. Write down the unrounded values on your paper to show what you are using, then round only the final equation.
将中间值保存在计算器中，不要四舍五入。在纸上写下未舍入的数值以展示所用的数字，只对最终方程进行舍入。
7. Standardise Normal Distribution with Precision and State Continuity Correction | 精确标准化正态分布并写明连续性校正
The 2019 Unit 5 paper asked for the probability that a normally distributed variable took a value greater than 15. Examiners expected the standardisation step to be clearly shown: Z = (15 − μ)/σ. Candidates who wrote only a calculator command without the Z-score lost the method mark. Additionally, when using a normal approximation to a binomial, the mark scheme awarded an explicit mark for the continuity correction, e.g., P(X > 10) ≈ P(Y > 10.5).
2019年单元5试卷要求计算正态分布变量大于15的概率。考官期望清晰展示标准化步骤：Z = (15 − μ)/σ。只写计算器命令而不写Z分的考生丢掉了方法分。此外，用正态近似二项分布时，评分方案专门为连续性校正设定了一分，例如P(X > 10) ≈ P(Y > 10.5)。
Write the standardisation line every time, even if your calculator gives the answer directly. For approximations, bracket the continuity correction statement to draw the examiner’s attention and ensure that mark is not overlooked.
每次都要写下标准化这一步，即使计算器可以直接给出答案。对于近似计算，用括号标出连续性校正的语句，吸引考官的注意，确保这一分不被遗漏。
8. Choose and Justify Statistical Diagrams Correctly | 正确选择并合理解释统计图表
A June 2019 question gave grouped frequency data and asked for a suitable diagram. The mark scheme accepted both histograms and cumulative frequency curves, but required justification: “histogram – because data is continuous and grouped” or “cumulative frequency curve – to show median.” Candidates who merely drew a bar chart lost the justification mark.
2019年6月的一道题给出了分组频数数据，要求选择合适的图表。评分方案同时接受直方图和累积频率曲线，但需要说明理由：“直方图——因为数据是连续且分组的”或“累积频率曲线——用以显示中位数”。只绘制条形图的考生丢掉了理由分。
| Diagram Type | Suitable For | Justification Key Phrase |
|---|---|---|
| Histogram | Continuous, grouped data | “area proportional to frequency” |
| Cumulative Frequency Curve | Estimating median, quartiles | “shows cumulative totals” |
| Box Plot | Comparing distributions | “displays outliers and spread” |
Memorise a one-line justification for each diagram type. The 2019 scheme suggests that a correct diagram without justification rarely scores full marks.
记住每种图表类型的一行理由。2019年的评分方案表明，没有理由的正确图表很少能拿满分。
9. Use Class Boundaries, Not Midpoints, for Cumulative Frequency | 累积频率使用组边界而非组中值
A frequent error in the June 2019 Unit 5 paper was plotting cumulative frequency at class midpoints instead of upper class boundaries. The mark scheme deducted the plotting mark for any point not placed exactly at the upper boundary, such as 40.5 for the class 31−40. Candidates who assumed the intervals were 31−40 meant exactly 31 to 40 (and plotted at 40) also lost out when the data implied a continuous scale.
2019年6月单元5试卷中一个频繁出现的错误是将累积频率绘制在组中值而非上组边界。评分方案对未精确绘制在上边界（例如31−40组应在40.5）的任何点扣掉了描点分。那些认为区间31−40就代表31到40（并画在40）的考生，在数据暗示连续尺度时也同样失分。
Before plotting, check if the data is given as inequalities like 0 ≤ x < 10. The upper boundary is then 10. If it is simply "1-10", assume 0.5-10.5 unless stated otherwise. Always label axes with "(upper class boundary)" to show your understanding.
在绘图之前，检查数据是否用不等式如0 ≤ x < 10表示。那么上边界就是10。如果只是“1-10”，除非另有说明，应假设为0.5-10.5。务必在数轴上标注“（上组边界）”来展示你的理解。
10. Present Work Clearly to Maximise Method Marks | 清晰呈现解题过程以获得最多方法分
The June 2019 mark scheme repeatedly stressed that method marks are awarded for a correct process, even if the final answer is wrong. For a 5-mark question on probability, the scheme broke the marks into: stating the formula (1), substituting numbers correctly (1), simplifying (1), finding a critical Z or probability (1), and the final answer (1). Candidates who wrote only the final answer scored at most 1 mark.
2019年6月的评分方案一再强调，方法分是奖励正确过程的，即使最终答案有误。一道5分的概率题，方案将分数拆分成了：写出公式（1分），正确代入数字（1分），化简（1分），找到关键Z值或概率（1分），以及最终答案（1分）。只写最终答案的考生最多只得1分。
Adopt a “step by step” mantra: formula → substitution → calculation → final value. Leave your calculator steps visible, such as writing “using GDC, Z = 1.96”. Even a blank space where a step has been skipped can cause you to lose the benefit of the doubt.
请坚持“分步走”原则：公式 → 代入 → 计算 → 最终数值。让计算器步骤可见，例如写下“使用GDC，Z = 1.96”。即便某个步骤被跳过留下空白，也可能让你失去得分的怀疑机会。
11. Handle “Give a Reason” Questions with Concise Contextual Accuracy | 用简洁且切合情境的表述回答“给出理由”题
Several marks in the 2019 paper were reserved for “give a reason” or “comment” style questions, for instance, why a linear regression model might not be appropriate. The mark scheme accepted: “the scatter diagram shows a curved pattern” or “the residual plots show a pattern.” Vague responses like “it does not fit” scored nothing.
2019年试卷中有好几分是预留给“给出理由”或“评论”类问题的，比如为什么线性回归模型可能不合适。评分方案接受：“散点图显示弯曲形态”或“残差图显示出规律”。而像“它不合适”这样含糊的回答则一分未得。
Always return to the data given. If a question shows a scatter diagram with an obvious curve, say “the points follow a curve, not a straight line.” Use statistical vocabulary: “heteroscedastic,” “non-linear,” or “pattern in residuals” where appropriate.
一定要回到给出的数据上。如果题目展示的散点图有明显曲线，就说“这些点沿曲线分布，而非直线”。适当使用统计术语：“异方差性”、“非线性”或“残差中的模式”。
12. Review Your Work Using the Mark Scheme Mentality | 用评分方案思维检查你的试卷
The best way to internalise the June 2019 scoring habits is to mark your own past paper using the official mark scheme. As you mark, notice how many times you rewarded yourself for something other than the final answer. This builds an instinct to write down every formula and intermediate number. In the actual exam, that instinct turns into easy marks.
内化2019年6月评分习惯的最佳方式，是用官方评分方案给自己的历年真题打分。在打分时，留意自己有多少次因为最终答案之外的内容给自己加分。这能培养你写下每一个公式和中间数字的本能。在真实考试中，这种本能就会转化为唾手可得的分数。
After each practice paper, make a checklist of the type of method marks you missed. Common 2019 entries include: “forgot to state assumption,” “rounded too early,” and “did not give units.” Eliminating these recurring errors can easily lift your grade by one boundary.
每一次做完练习卷后，列一份你所错失的方法分类型清单。2019年常见的条目包括：“忘记陈述假设”、“过早四舍五入”以及“未写单位”。消除这些反复出现的错误，就能轻松把你的成绩拉升一个等级。
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