A-Level Maths Unit 5 Mark Scheme Jan 22: Common Mistakes | A-Level数学 Unit 5 2022年1月评分方案易错点总结

📚 A-Level Maths Unit 5 Mark Scheme Jan 22: Common Mistakes | A-Level数学 Unit 5 2022年1月评分方案易错点总结

The January 2022 Unit 5 (Statistics 1) exam revealed several recurring errors that cost students valuable marks. By analysing the official mark scheme, we have distilled the most common pitfalls, from misreading histograms to mishandling normal distribution tables. This article pinpoints these errors and shows you how to avoid them in your revision.

2022年1月Unit 5（统计学1）考试暴露了许多学生反复出现并因此失分的错误。通过分析官方评分方案，我们提炼出最常见的失分点，涵盖从直方图误读到正态分布表使用不当等问题。本文指出这些错误，并教你如何在复习中避免。

1. Histograms: Frequency Density Confusion | 直方图：频数密度混淆

In histograms, the height of each bar represents frequency density, not frequency. Many candidates mistakenly plot frequency on the vertical axis, especially when class widths are unequal. This leads to incorrectly shaped diagrams and wrong area calculations when estimating frequencies.

在直方图中，条形的高度代表频数密度，而非频数。许多考生错误地在纵轴上标出频数，尤其在组距不相等时。这会导致图形形状错误，并在估计频数时计算出错。

The mark scheme clearly requires the area to be proportional to frequency. Always compute frequency density = frequency ÷ class width. If a bar has class width 10 and frequency 15, the density is 1.5, not 15. Double-check your axes labels.

评分方案明确要求面积与频数成正比。务必计算频数密度 = 频数 ÷ 组距。若某组组距为10、频数为15，则密度为1.5，而非15。务必检查坐标轴标签。

2. Stem-and-Leaf Diagrams: Missing Keys and Ordering | 茎叶图：遗漏键与排序

A surprising number of students lost marks simply because they omitted a key for their stem-and-leaf diagram. Without a key indicating what the stem and leaf units represent, the diagram is meaningless. For example, ‘4 | 2 means 42’ is essential.

有相当多的学生仅仅因为遗漏了茎叶图的键（key）而失分。没有键来说明茎和叶的单位，图形便毫无意义。例如 ‘4 | 2 表示 42’ 是必不可少的。

Additionally, leaves must be ordered in ascending order from left to right, and stems must be arranged vertically in order. Leaving leaves unsorted or inserting a stem without leaves (except when it represents an empty class) can cost marks.

此外，叶必须从左到右按升序排列，且茎需按序垂直排列。叶未排序或插入空茎（除非代表空组）都会导致扣分。

3. Measures of Spread: Sample vs Population Variance | 离散量数：样本与总体方差混淆

A common slip is using the wrong denominator when calculating variance. The mark scheme often expects the sample variance formula s² = Σ(x − x̅)²/(n − 1) when data are a sample. Many candidates use the population formula σ² = Σ(x − μ)²/N, losing marks if the context clearly refers to a sample.

常见的错误是计算方差时使用了错误的分母。当数据为样本时，评分方案通常要求使用样本方差公式 s² = Σ(x − x̅)²/(n − 1)。许多考生误用总体公式 σ² = Σ(x − μ)²/N，一旦上下文明确指出是样本便会失分。

Here is a quick comparison of typical mistakes and the correct approach:

下面快速对比典型错误与正确做法：

Always read the question carefully: words like ‘random sample’, ‘a sample of’, or ‘estimate the variance’ suggest you should use (n − 1). Remember, Σ(x − x̅)² can be computed as Σx² − (Σx)²/n. Misapplication of this shortcut was another frequent source of error.

务必仔细读题：”随机样本”、”…的样本” 或 “估计方差” 等措辞表明应使用 (n − 1)。记住，Σ(x − x̅)² 可通过 Σx² − (Σx)²/n 计算。对该捷径的错误应用也是常见的错误来源。

4. Linear Regression: Mixing Up x and y | 线性回归：混淆自变量与因变量

In the regression line y = a + bx, it is critical to correctly identify the explanatory (x) and response (y) variables. Many Jan 2022 candidates mislabelled them and consequently computed the wrong gradient b = Sxy/Sxx. The mark scheme penalises using Syy or swapping variables heavily.

在回归线 y = a + bx 中，正确识别解释变量(x)和响应变量(y)至关重要。2022年1月的许多考生误标了变量，导致算错斜率 b = Sxy/Sxx。评分方案对使用 Syy 或调换变量的情况扣分很重。

Moreover, when making predictions, students sometimes extrapolate beyond the data range without commenting on unreliability

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