📚 Year 7 SQA Statistics: Unit Test Mock Paper Analysis | 七年级SQA统计：单元测试模拟卷解析
This article takes you through a full mock paper for a Year 7 SQA Statistics unit test. Each question is explained step by step, covering key topics such as tally charts, bar charts, mean, median, mode, range, probability and stem-and-leaf diagrams. Use this analysis to check your understanding and sharpen your exam technique.
本文将带你完整解析一份七年级 SQA 统计单元测试模拟卷。每道题目都配有逐步讲解，涵盖划记表、条形图、平均数、中位数、众数、极差、概率和茎叶图等核心知识点。通过这份解析来检查你的理解并提升应考技巧。
1. Tally Charts and Frequency Tables | 划记表与频数表
Question: A survey asked 30 students their favourite fruit. The results are: Apple 8, Banana 5, Orange 7, Grape 4, Strawberry 6. Complete the tally chart and frequency table. Then state which fruit is the most popular.
问题：一项调查询问了30名学生最喜欢的水果。结果如下：苹果8，香蕉5，橙子7，葡萄4，草莓6。完成划记表和频数表。然后指出哪种水果最受欢迎。
For Apple, draw eight tally marks as two groups of five (|||| and |||). The frequency is 8.
苹果的划记可画成两组五条（|||| 和 |||），频数为8。
For Banana, five tally marks make one gate (~~||||~~). Frequency 5.
香蕉的划记为五条一组（~~||||~~），频数5。
Orange gets seven: one gate plus two strokes (~~||||~~ ||). Frequency 7.
橙子为七条：一组加两竖（~~||||~~ ||），频数7。
Grape has four strokes (||||). Frequency 4.
葡萄四条竖线（||||），频数4。
Strawberry uses one gate and one stroke (~~||||~~ |). Frequency 6.
草莓一组加一竖（~~||||~~ |），频数6。
The fruit with the highest frequency is Apple, so it is the most popular.
频数最高的水果是苹果，因此它最受欢迎。
2. Drawing and Reading Bar Charts | 绘制与解读条形图
Using the data from Question 1, draw a bar chart. Label the axes clearly and give the chart a title. Then use your chart to find the difference between the highest and lowest frequencies.
使用第1题的数据绘制条形图。给坐标轴清晰标注并为图表起标题。然后利用图表找出最高频数与最低频数的差值。
The horizontal axis shows fruit types; the vertical axis shows frequency from 0 to 10. Draw bars of equal width with heights 8, 5, 7, 4, 6. Title: 'Favourite Fruit of Year 7 Students'.
横轴表示水果种类，纵轴表示频数（0到10）。画出等宽的长条，高度分别为8、5、7、4、6。标题为’七年级学生最喜欢的水果’。
, the tallest bar is Apple (8) and the shortest is Grape (4). The difference is 8 - 4 = 4.
从条形图看，最高条形为苹果(8)，最矮为葡萄(4)。差值为 8 − 4 = 4。
Always remember: bars must not touch, and the vertical scale must start at zero.
始终记住：条形之间不能接触，纵轴刻度必须从零开始。
3. Finding the Mode | 求众数
Question: What is the mode of the favourite fruit data? Explain why.
问题：最喜欢水果数据的众数是什么？说明理由。
The mode is the value that appears most often. Frequencies are: Apple 8, Banana 5, Orange 7, Grape 4, Strawberry 6. Apple has the highest frequency, so the mode is 'Apple'.
众数是出现次数最多的值。频数为：苹果8，香蕉5，橙子7，葡萄4，草莓6。苹果频数最高，所以众数是“苹果”。
If two fruits both had the highest frequency, the data would be bimodal and we would give both. Here, only Apple is the mode.
如果有两种水果同时具有最高频数，数据就是双峰的，我们会写出两者。这里只有苹果是众数。
4. Calculating the Mean | 计算平均数
Find the mean number of students per fruit from the survey data. Give your answer correct to one decimal place if necessary.
根据调查数据计算每种水果平均被选择的学生人数。如需要，答案保留一位小数。
First, total number of students: 8 + 5 + 7 + 4 + 6 = 30. Number of fruit types is 5.
首先，总学生数：8 + 5 + 7 + 4 + 6 = 30。水果种类数是5。
Mean = 30 ÷ 5 = 6
平均数 = 30 ÷ 5 = 6
The mean number of students choosing each fruit type is exactly 6. There is no need to round.
平均每种水果被选择的人数为正好6，无需四舍五入。
Notice: The mean does not have to be one of the actual data values – here, 6 is not a frequency for any individual fruit but represents the centre of the data.
注意：平均数不必是实际数据值之一——这里6并非任何一个水果的频数，但它代表了数据的中心。
5. Range of Frequencies | 频数的极差
Calculate the range of the frequencies from the favourite fruit table.
计算最喜欢水果数据表中频数的极差。
Range = Highest frequency − Lowest frequency
极差 = 最高频数 − 最低频数
Range = 8 − 4 = 4
极差 = 8 − 4 = 4
The range tells us how spread out the frequencies are. A small range suggests the data are fairly consistent, which is true here as choices are spread across five fruits.
极差告诉我们频数的分散程度。较小的极差说明数据相当一致，这里五种水果的选择分布正是如此。
6. Comparing Groups Using the Median | 利用中位数比较组别
Two classes took a short quiz. Scores out of 20: Class A – 12, 15, 14, 13, 16, 14. Class B – 10, 18, 12, 13, 15, 12. Find the median score for each class and comment on which class performed more consistently.
两个班级进行了一次小测验，满分20。A班成绩：12, 15, 14, 13, 16, 14。B班成绩：10, 18, 12, 13, 15, 12。分别求每个班级成绩的中位数，并说明哪个班级表现更稳定。
4, 14, 15, 16. Six scores, median lies between the 3rd and 4th values. (14 + 14) ÷ 2 = 14.
将A班排序：12, 13, 14, 14, 15, 16。六个数据，中位数在第3和第4个值之间。(14 + 14) ÷ 2 = 14。
Order Class B: 10, 12, 12, 13, 15, 18. Median is (12 + 13) ÷ 2 = 12.5.
将B班排序：10, 12, 12, 13, 15, 18。中位数 = (12 + 13) ÷ 2 = 12.5。
Both classes have the same median? Check: A median 14, B median 12.5. So Class A has higher central tendency.
两班中位数不同：A班14，B班12.5。因此A班的集中趋势更高。
range = 18 − 10 = 8. Class A has a much smaller range, so its scores are more consistent.
判断稳定性要看极差。A班极差 = 16 − 12 = 4；B班极差 = 18 − 10 = 8。A班极差小很多，因此成绩更稳定。
7. Introduction to Probability | 概率初步
A bag contains 4 red balls, 3 blue balls and 2 green balls. One ball is taken at random. What is the probability it is red? Write your answer as a fraction in its simplest form.
一个袋子里有4个红球、3个蓝球和2个绿球。从袋中随机取出一个球。取出红球的概率是多少？用最简分数表示。
Total number of balls = 4 + 3 + 2 = 9. Number of red balls = 4.
总球数 = 4 + 3 + 2 = 9。红球数量 = 4。
P(red) = 4 / 9
P(红球) = 4 / 9
The fraction is already in its simplest form since 4 and 9 have no common factors other than 1.
这个分数已经是最简形式，因为4和9除了1没有其他公因数。
Probability values always lie between 0 and 1 inclusive. A probability of 4/9 means the event is less than even chance but still quite likely.
概率值总是在0到1之间（含0和1）。4/9意味着事件发生的可能性略小于一半，但仍相当可能。
8. Probability with Spinners | 转盘概率
A spinner has 8 equal sections: 3 blue, 2 red, and 1 each of yellow, green and purple. Find the probability of landing on blue. Also find the probability of not landing on red.
一个转盘被分成8个相等的扇形：3个蓝色，2个红色，黄色、绿色和紫色各1个。求指针停在蓝色的概率。再求不停在红色的概率。
) = 3/8. This is because there are 3 favourable outcomes out of 8 equally likely sections.
P(蓝色) = 3/8，因为有3个有利结果，总共8个等可能的扇形。
For 'not red' unt all sections that are not red: 8 − 2 = 6. So P(not red) = 6/8 = 3/4 after simplifying.
关于“非红色”，数出所有不是红色的扇形：8 − 2 = 6。所以P(非红) = 6/8 = 3/4，化简后。
Alternatively, P(not red) = 1 − P(red) = 1 − 2/8 = 1 − 1/4 = 3/4. Both methods are valid.
另一种解法：P(非红) = 1 − P(红) = 1 − 2/8 = 1 − 1/4 = 3/4。两种方法都正确。
9. Stem-and-Leaf Diagrams | 茎叶图
The times (in minutes) spent on homework by 8 students are: 30, 45, 20, 60, 35, 40, 25, 50. Draw an ordered stem-and-leaf diagram and find the median.
8名学生做作业所花的时间（分钟）为：30, 45, 20, 60, 35, 40, 25, 50。画出一个有序茎叶图并求出中位数。
Use the tens digit as the stem and the units digit as the leaf. Stems: 2, 3, 4, 5, 6.
把十位数字作为茎，个位数字作为叶。茎为：2, 3, 4, 5, 6。
Leaves for stem 2: 0, 5 (from 20,25). Stem 3: 0, 5. Stem 4: 0, 5. Stem 5: 0. Stem 6: 0. Order leaves in ascending order.
茎2的叶：0, 5（来自20, 25）。茎3：0, 5。茎4：0, 5。茎5：0。茎6：0。将叶按升序排列。
Complete stem-and-leaf:
| 2 | 0 5 |
| 3 | 0 5 |
| 4 | 0 5 |
| 5 | 0 |
| 6 | 0 |
Key: 2|0 means 20 minutes.
图例：2|0 表示20分钟。
, 50, 60. Eight values, so median is average of 4th and 5th: (35 + 40) ÷ 2 = 37.5 minutes.
根据图示列出有序数据：20, 25, 30, 35, 40, 45, 50, 60。共8个值，中位数为第4和第5个值的平均数：(35 + 40) ÷ 2 = 37.5分钟。
10. Interpreting Pie Charts | 饼图解读
A pie chart shows favourite sports: Football 40%, Basketball 25%, Tennis 15%, Others 20%. There are 200 students surveyed. How many students prefer football? Which sport is least popular?
一个饼图显示了最喜欢的运动：足球40%，篮球25%，网球15%，其他20%。共有200名学生接受调查。有多少学生偏爱足球？哪种运动最不受欢迎？
Number for football = 40% of 200 = 0.40 × 200 = 80 students.
足球人数 = 200的40% = 0.40 × 200 = 80名学生。
The smallest sector is Tennis at 15%, so tennis is the least popular sport among the three named categories. 'Others' is a combined category so we focus on the named sports when identifying the least popular single sport.
占比最小的扇形是网球15%，因此在三个已命名的运动类别中网球最不受欢迎。“其他”是合并类别，所以在确定最不受欢迎的单项运动时我们关注已命名的运动。
Check that percentages add to 100%: 40+25+15+20 = 100. This confirms the pie chart is valid.
验证百分比之和：40+25+15+20=100，说明饼图有效。
11. Designing a Survey | 设计调查方案
Design a survey to find out your classmates’ favourite film genre. Describe your data collection sheet, how you will record responses, and which chart you would use to display the results.
设计一项调查，了解同学们最喜欢的电影类型。描述你的数据收集表、如何记录回答，以及你会用哪种图表来展示结果。
I would create a tally chart with genres: Action, Comedy, Horror, Sci-Fi, Animation, Other. Ask each classmate to choose one genre and record using tallies.
我会制作一个划记表，包含类型：动作、喜剧、恐怖、科幻、动画、其他。询问每位同学选择一种类型并用划记记录。
After collecting data, I would total the frequencies and draw a bar chart with genre on the x-axis and frequency on the y-axis. The bar chart makes it easy to compare the popularity of different genres.
收集数据后，我会统计频数并绘制条形图，x轴为电影类型，y轴为频数。条形图便于比较不同电影类型的受欢迎程度。
To ensure the survey is fair, I would ask every student in the class to take part, so the sample represents the whole class.
为保证调查公平，我会让班上每位学生都参与，这样样本能代表整个班级。
12. Common Mistakes and Top Tips | 常见错误与提分技巧
When sitting a statistics test, avoid these frequent errors: forgetting to label axes on charts; counting tally marks incorrectly; confusing the mean with the median; and writing probabilities unsimplified.
参加统计测验时，要避免这些常见错误：忘记给图表坐标轴加标签；划记计数出错；混淆平均数和中位数；概率答案未化简。
Always show your working, even when you think the answer is obvious. Marks are often awarded for method, not just the final number.
务必写出解题步骤，即使你认为答案很明显。分数往往针对方法给出，而不仅仅是最终数字。
For probability, check that fractions add correctly when all outcomes are considered. For charts, use a ruler and sharp pencil. Finally, read the question carefully – the word 'not' changes everything.
对于概率题，检查所有可能结果对应的分数之和是否正确。画图时使用直尺和削好的铅笔。最后，仔细读题——一个“不”字会彻底改变问题的意思。
Published by TutorHao | Statistics Revision Series | aleveler.com
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