📚 Year 7 SQA Statistics: Unit Test Mock Paper Walkthrough | Year 7 SQA 统计：单元测试模拟卷解析
This walkthrough covers the key question types found in a typical Year 7 SQA Statistics unit test. The mock paper includes interpreting bar charts and pie charts, calculating averages and range, working with frequency tables, drawing line graphs, and applying simple probability. Each section below breaks down one test question with a detailed bilingual explanation, helping you understand exactly what examiners are looking for and how to avoid common mistakes.
本文解析了Year 7 SQA 统计单元测试模拟卷中的典型题目。试卷内容涵盖条形图与饼图的解读、平均数与极差的计算、频数表、折线图绘制以及简单概率的应用。以下每个小节都针对一道模拟试题，提供中英双语详细解析，帮助你理解评分标准并避开常见错误。
1. Interpreting Bar Charts | 解读条形图
Question 1 showed a bar chart of favourite sports among 50 pupils. The bars for football, netball, swimming, and tennis had frequencies of 18, 12, 14, and 6. Pupils were asked to name the most popular sport and find how many more pupils chose football than tennis.
第1题展示了一幅50名学生最喜爱运动的条形图。足球、篮网球、游泳和网球的频数分别为18、12、14和6。题目要求学生找出最受欢迎的运动，并计算选择足球的人数比选择网球的多多少。
Reading the vertical axis carefully shows the football bar reaches 18, while tennis reaches 6. The difference is 18 − 6 = 12 pupils. Football is the most popular because it has the tallest bar. A common mistake is misreading the scale — always check that each grid line equals 1 or 2 units.
仔细观察纵轴，足球的条形高度为18，网球为6。两者相差18 − 6 = 12名学生。足球最受欢迎，因为条形柱最高。常见错误是读取刻度不当 —— 务必确认每个网格线代表1还是2个单位。
2. Calculating Mean, Median, and Mode | 计算平均数、中位数与众数
The test gave a set of spelling test scores: 7, 10, 6, 8, 7, 9, 7. Students had to find the mean, median, and mode. These three measures summarise a data set in different ways.
试卷给出一组拼写测验分数：7, 10, 6, 8, 7, 9, 7。要求学生求出平均数、中位数和众数。这三种统计量从不同角度概括了一组数据。
To find the mean, add all values: 7+10+6+8+7+9+7 = 54. Divide by the number of scores: 54 ÷ 7 ≈ 7.71 (to two decimal places). The mode is the most frequent value, which is 7. For the median, first order the data: 6, 7, 7, 7, 8, 9, 10. The middle value is the 4th score, so the median is 7.
求平均数时，先把所有分数相加：7+10+6+8+7+9+7 = 54，再除以分数的个数54 ÷ 7 ≈ 7.71（保留两位小数）。众数是出现次数最多的值，此处为7。计算中位数时，先将数据排序：6, 7, 7, 7, 8, 9, 10。中间位置是第4个分数，因此中位数为7。
Always check that you have written the data in ascending order before finding the median. Some questions also ask which average best represents the data — here the mean is slightly higher because of one large score (10), so the median or mode might be more typical.
记得在求中位数前将数据按升序排列。有些问题还会询问哪个平均数最能代表数据 —— 这里由于存在一个较高的分数（10），平均数被拉高，因此中位数或众数可能更有代表性。
3. Understanding Range | 理解极差
Using the same spelling scores, Question 3 asked for the range. The range shows how spread out the data is. It is found by subtracting the smallest value from the largest.
仍使用上述拼写分数，第3题要求计算极差。极差反映数据的分散程度，用最大值减去最小值得到。
Largest score = 10, smallest = 6, so the range is 10 − 6 = 4. A range of 4 tells us the scores varied only a little. If the range had been very large, it would indicate more inconsistency.
最大值 = 10，最小值 = 6，因此极差为10 − 6 = 4。极差为4说明分数波动不大。若极差很大，则表明成绩波动较大。
Common errors include mixing up the order (calculating 6 − 10) or forgetting to use the correct extremes when data is not sorted. Remember: Range = Maximum − Minimum, always positive or zero.
常见错误包括搞错相减顺序（如计算6 − 10），或在数据未排序时用错极值。请记住：极差 = 最大值 − 最小值，结果总是非负数。
4. Pie Charts and Proportions | 饼图与比例
Question 4 presented a pie chart showing how 120 pupils travel to school: Walk 90°, Bus 120°, Bike 60°, Car 90°. The task was to work out the number of pupils who walk and the fraction who travel by bus.
第4题呈现一张饼图，展示120名学生的上学交通方式：步行90°、公交120°、自行车60°、小汽车90°。题目要求计算步行的学生人数，以及乘公交的学生所占比例。
First, note that the whole pie is 360°. The walking sector is 90°, which is 90/360 = 1/4 of the circle. Number walking = 1/4 × 120 = 30 pupils. The bus sector is 120°, so the fraction is 120/360 = 1/3. To check: 1/3 of 120 = 40 pupils. This is a proportional reasoning skill often tested in SQA papers.
首先，整个饼图为360°。步行部分为90°，占总体的90/360 = 1/4。步行人数 = 1/4 × 120 = 30人。公交部分为120°，所占比例为120/360 = 1/3。验算：1/3 × 120 = 40人。这属于比例推理能力，SQA试卷中经常考查。
If the pie chart uses percentages instead of angles, the same logic applies: multiply the percentage (as a decimal) by the total. For example, 25% × 120 = 30. Always write fractions in their simplest form to gain full marks.
如果饼图使用百分比而非角度，逻辑相同：用百分比（转换为小数）乘以总数。例如，25% × 120 = 30。务必以最简分数作答，才能获得满分。
5. Frequency Tables and Tally Charts | 频数表与计数符号图
Question 5 gave raw data on the number of books read by 25 pupils in a month: 0,1,0,2,1,3,2,1,0,4,2,1,0,3,1,2,4,1,0,2,3,1,1,2,0. Pupils had to complete a tally and frequency table, then draw a bar chart.
第5题给出25名学生一个月内阅读书籍数量的原始数据：0,1,0,2,1,3,2,1,0,4,2,1,0,3,1,2,4,1,0,2,3,1,1,2,0。要求学生完成一张计数符号与频数表，并画出条形图。
Organise the data using tally marks in groups of five. The frequencies were: 0 books → 6, 1 book → 8, 2 books → 6, 3 books → 3, 4 books → 2. Always count carefully and double-check the total matches the number of data items (25). The bar chart must have labelled axes, equal bar widths, and an appropriate scale.
用五个一组画计数符号整理数据。频数分别为：0本书 → 6人，1本书 → 8人，2本书 → 6人，3本书 → 3人，4本书 → 2人。务必仔细计数，再次核对频数总和是否等于数据总数（25）。条形图需注明坐标轴，条形等宽，并选用合适刻度。
Examiners often deduct marks if bars are not separated by equal gaps or if the vertical axis does not start at zero. Also, labelling ‘Number of books’ and ‘Frequency’ on the correct axes is essential.
考官常因条形间未留均匀空隙或纵轴未从零开始而扣分。此外，正确标注“书籍数量”与“频数”到对应数轴上极为重要。
6. Data Collection Methods | 数据收集方法
One extended response item asked pupils to design a fair question for a survey on screen time and explain why a given question was biased: ‘Do you agree that spending too many hours on your phone is bad?’
一道简答题要求学生为一项关于屏幕时间的调查设计一个公平的问题，并解释为何以下问题存在偏差：“你是否同意在手机上花太多小时是有害的？”
A fair question should be neutral, such as ‘How many hours per day do you spend on your phone?’ with clear time bands (0–1, 1–3, 3–5, more than 5). The original question is leading — it pushes the respondent towards agreeing, which creates bias. Also, data collected directly by the researcher is primary data; using existing records is secondary.
公平的问题应保持中立，例如“你每天在手机上花费多少小时？”并给出明确的时间段（0–1, 1–3, 3–5, 5小时以上）。原问题带有引导性——它暗示受访者应当同意，从而产生偏差。另外，由研究者直接收集的数据是一手数据；使用现有记录则属于二手数据。
When writing survey questions, avoid emotional words like ‘bad’ or ‘waste’. Use multiple-choice options to make analysis easier. Always mention whether the data is primary or secondary, as this is part of the SQA statistics criteria.
设计调查问题时，避免使用“坏”或“浪费”等带有感情色彩的词语。使用选择题选项可使分析更简便。务必说明数据是一手还是二手，这属于SQA统计考查的标准。
7. Drawing Line Graphs | 绘制折线图
Question 7 provided a table of maximum daily temperatures over a week: Mon 8°C, Tue 10°C, Wed 9°C, Thu 12°C, Fri 14°C, Sat 13°C, Sun 11°C. The task was to draw a line graph and describe the trend.
第7题提供了一周每日最高气温表：周一8°C，周二10°C，周三9°C，周四12°C，周五14°C，周六13°C，周日11°C。要求绘制折线图并描述趋势。
Plot the points with the day on the horizontal axis and temperature on the vertical axis. Use a continuous scale from at least 0°C to 16°C. Join the points with straight lines. The trend shows a steady rise from Monday to Friday, a slight dip on Saturday, and a further decrease on Sunday. Overall, the mid-week period was warmer.
将日期标在横轴、温度标在纵轴，在坐标上描点。纵轴刻度至少从0°C延伸至16°C。用线段将点连接。趋势显示从周一到周五气温稳步上升，周六轻微回落，周日继续下降。总体来说，周中较暖。
Pupils often forget to plot points accurately (e.g. using the middle of the day label) or fail to label the axes with units. For describing trends, use phrases like ‘increases steadily’, ‘remains constant’, or ‘peaks at’.
学生常会遗忘精确描点（例如应将点标在日期的正中间位置）或忘记在坐标轴上标注单位。描述趋势时，可使用诸如“稳步上升”、“保持不变”或“在…达到峰值”等表述。
8. Interpreting Tables | 解读表格
A two-way table in Question 8 showed the number of boys and girls in three classes who achieved a merit award: Class 1A (Boys 7, Girls 9), Class 1B (Boys 10, Girls 8), Class 1C (Boys 6, Girls 11). Questions included finding the total number of merits in Class 1B and the proportion of boys receiving merits across all classes.
第8题中的双向表格展示了三个班级获得优秀奖的男女生人数：1A班（男生7，女生9），1B班（男生10，女生8），1C班（男生6，女生11）。问题包括计算1B班获奖的总人数，以及所有班级中获奖男生的比例。
Total in 1B = 10 + 8 = 18 merits. Overall total merits = (7+9)+(10+8)+(6+11) = 51. Total boys = 7+10+6 = 23. Proportion of merits that went to boys = 23 out of 51, which can be written as the fraction 23/51. To convert to a percentage, calculate (23 ÷ 51) × 100 ≈ 45.1%.
1B班获奖总数 = 10 + 8 = 18。总获奖数 = (7+9)+(10+8)+(6+11) = 51。男生总数 = 7+10+6 = 23。男生获奖的比例为51人中的23人，可写成分数23/51。转换为百分比，计算 (23 ÷ 51) × 100 ≈ 45.1%。
Always read the row and column headings carefully. A practical check: the proportion of girls = 1 − 23/51 = 28/51, and 28+23 = 51, confirming our addition. In SQA exams, rounding should be to one decimal place when percentages are involved unless specified otherwise.
务必仔细阅读行与列的标题。可进行实际验算：女生比例 = 1 − 23/51 = 28/51，且28+23 = 51，证明加法正确。SQA考试中，涉及百分比时通常保留一位小数，除非另有说明。
9. Probability from Data | 基于数据的概率
The final question described an experiment where a counter was drawn from a bag 30 times (replaced each time). Red appeared 12 times, blue 10 times, and green 8 times. Pupils needed to estimate the probability of drawing a red counter and state why the experiment might not give the exact theoretical probability.
最后一题描述了一项实验：从一个袋子中抽取彩球30次（每次放回）。红色出现12次，蓝色10次，绿色8次。学生需要估计抽出红色彩球的概率，并说明为何实验可能无法给出精确的理论概率。
Estimated probability of red = 12/30 = 2/5 = 0.4. This is an experimental probability based on observed outcomes. The more trials we do, the closer the estimate usually gets to the true probability if the process is fair. However, with only 30 trials, the estimate might not be exact; repeating the experiment many times would give a more reliable result.
红色的估计概率 = 12/30 = 2/5 = 0.4。这是基于观测结果的实验概率。实验次数越多，如果过程公平，估计值通常越接近真实概率。然而，仅有30次试验，估计值可能不精确；多次重复实验会得到更可靠的结果。
To express probability, always simplify fractions and consider using decimals. A full answer also explains that chance variation means the results of a small number of trials may differ from the underlying probability. This connects to the concept of randomness.
表达概率时，一定要约简分数，也可考虑使用小数。完整的解答还会解释，机会变异意味着少量试验的结果可能与潜在概率不同。这与随机性的概念相关。
Published by TutorHao | Statistics Revision Series | aleveler.com
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