Year 8 WJEC Statistics: Mock Unit Test Walkthrough | 8年级WJEC统计：单元测试模拟卷解析

📚 Year 8 WJEC Statistics: Mock Unit Test Walkthrough | 8年级WJEC统计：单元测试模拟卷解析

This article provides a detailed walkthrough of a typical Year 8 WJEC Statistics mock unit test. Each section breaks down a common question type, offering step-by-step solutions, essential tips, and common mistakes to avoid. Use this as your ultimate revision guide to strengthen your statistical skills and boost your confidence before the real test.

本文为一份典型的8年级WJEC统计单元测试模拟卷提供详细解析。每一节分析一个常见题型，给出分步解答、关键技巧以及需要避免的常见错误。把这篇文章作为你的终极复习指南，强化统计技能，在实际考试前提升信心。

1. Mean, Median, Mode and Range from a List | 从列表中求平均数、中位数、众数和极差

Question 1 presented a small raw data set: 5, 8, 12, 8, 15, 9. Students were asked to calculate the mean, median, mode and range. The mean is found by adding all values and dividing by the number of values: (5 + 8 + 12 + 8 + 15 + 9) ÷ 6 = 57 ÷ 6 = 9.5. To find the median, first order the data: 5, 8, 8, 9, 12, 15. With six values, the median is the mean of the 3rd and 4th ordered values: (8 + 9) ÷ 2 = 8.5. The mode is the most frequent value, which is 8 since it appears twice. The range is the largest value minus the smallest: 15 − 5 = 10. Always write the median and mode as numbers, not positions, and remember to reorder for median.

问题1给出了一组原始数据：5, 8, 12, 8, 15, 9。要求学生计算平均数、中位数、众数和极差。平均数通过把所有数值相加再除以数值的个数得到：(5 + 8 + 12 + 8 + 15 + 9) ÷ 6 = 57 ÷ 6 = 9.5。要找到中位数，先把数据排序：5, 8, 8, 9, 12, 15。有六个数据，中位数是第3和第4个有序值的平均数：(8 + 9) ÷ 2 = 8.5。众数是出现最频繁的值，8出现了两次，所以众数是8。极差是最大值减最小值：15 − 5 = 10。务必把中位数和众数写成数值，而不是位置，并记得为求中位数重新排序。

---

2. Mean from a Frequency Table | 从频数表求平均数

Question 2 gave a frequency table showing the number of pets owned by families. The table had rows: 0 pets, 1 pet, 2 pets, 3 pets with frequencies 4, 7, 5, 2 respectively. To find the mean number of pets, a new column ‘Pets × Frequency’ is needed. Multiply each value by its frequency: 0×4=0, 1×7=7, 2×5=10, 3×2=6. Sum the frequency column to get total families: 4+7+5+2=18. Sum the ‘Pets × Frequency’ column: 0+7+10+6=23. Then mean = 23 ÷ 18 ≈ 1.28 pets. Many students forget to divide by the total frequency and mistakenly divide by the number of rows. Always use the total frequency as the denominator.

问题2给出了一个关于家庭拥有宠物数量的频数表。表格行分别为：0只宠物、1只宠物、2只宠物、3只宠物，频数分别是4、7、5、2。要计算宠物数量的平均数，需要增加一列“宠物数量×频数”。把每个值乘以它的频数：0×4=0, 1×7=7, 2×5=10, 3×2=6。把频数列相加得到总家庭数：4+7+5+2=18。把“宠物数量×频数”列相加：0+7+10+6=23。然后平均数 = 23 ÷ 18 ≈ 1.28只宠物。许多学生忘记除以总频数，而错误地除以行数。一定要用总频数作为分母。

---

3. Interpreting a Bar Chart | 条形图的解读

Question 3 provided a bar chart showing favourite fruits among 30 students. The bars for apple, banana, orange and grape had heights 8, 12, 6 and 4. One sub-question asked, ‘Which fruit is the mode?’ Since the highest bar represents the greatest frequency, banana is the mode. Another part asked for the fraction of students who chose orange. 6 out of 30 chose orange, which simplifies to 1/5. When interpreting bar charts, always check the vertical axis scale carefully; sometimes it does not start at zero, which can mislead comparisons.

问题3给出了一个体现30名学生最喜欢水果的条形图。代表苹果、香蕉、橙子和葡萄的条形高度分别为8、12、6和4。一个小题问“哪种水果是众数？”因为最高的条形代表最大频数，所以香蕉是众数。另一部分要求找出选择橙子的学生比例。30人中有6人选橙子，化简为1/5。解读条形图时，一定要仔细检查纵轴刻度；有时纵轴不从零开始，可能误导比较。

---

4. Constructing a Pie Chart | 构建饼图

Question 4 gave data on how students travel to school: walk 15, bus 9, cycle 6. Students had to calculate the angle for each sector. The total frequency is 15+9+6=30. Since a full circle has 360°, the multiplier is 360° ÷ 30 = 12° per student. Multiply each frequency by 12° to get sector angles: walk 15×12°=180°, bus 9×12°=108°, cycle 6×12°=72°. Check that the sum of angles equals 360° (180+108+72=360). Draw the pie chart with a compass and protractor, label each sector clearly and give the chart a title. Common errors include using the wrong multiplier and forgetting to add a title.

问题4给出学生上学交通方式的数据：步行15人、公交9人、骑车6人。学生需计算每个扇形的角度。总频数是15+9+6=30。因为整个圆为360°，乘数是360° ÷ 30 = 每人12°。每个频数乘以12°得到对应的扇形角：步行15×12°=180°，公交9×12°=108°，骑车6×12°=72°。检查角度总和是否等于360°（180+108+72=360）。用圆规和量角器画出饼图，清楚地标注每个扇形并给图表加上标题。常见错误包括使用错误的乘数和忘记添加标题。

---

5. Scatter Graphs and Correlation | 散点图与相关性

Question 5 asked students to plot a scatter graph of test scores in maths and science for 10 pupils and describe the correlation. After plotting the points, the pattern shows that as maths scores increase, science scores also tend to increase. This indicates a positive correlation. The question also asked to draw a line of best fit. The line should pass through the middle of the points, with roughly equal numbers of points above and below. It should not be forced through the origin. Using the line of best fit, students could estimate a science score for a pupil with a given maths score. Always use a sharp pencil and cross marks for plotted points.

问题5要求学生画出10名学生在数学和科学测试中得分的散点图，并描述相关性。描点之后，图案显示出随着数学成绩提高，科学成绩也往往提高。这表明存在正相关。此题还要求画出最佳拟合线。这条线应穿过点的中间，线上方和下方的点数大致相等。不应强行使直线通过原点。利用最佳拟合线，学生可以估算出某一数学成绩对应的科学成绩。作图中始终使用削尖的铅笔，并用叉号标记描点。

---

6. Line Graphs and Trend Analysis | 折线图与趋势分析

Question 6 displayed a line graph of maximum daily temperature over a week. The temperatures from Monday to Sunday were: 12°C, 14°C, 11°C, 15°C, 18°C, 20°C, 19°C. Students were asked, ‘Between which two consecutive days was the greatest increase in temperature?’ Calculate differences: Mon-Tue +2, Tue-Wed -3, Wed-Thu +4, Thu-Fri +3, Fri-Sat +2, Sat-Sun -1. The greatest increase was +4°C between Wednesday and Thursday. Another part asked for a description of the overall trend. There is a general upward trend over the week, despite a slight drop at the end. Never confuse line graphs with bar charts; line graphs show change over time.

问题6展示了一周内每日最高温度的折线图。周一到周日的温度分别为：12°C、14°C、11°C、15°C、18°C、20°C、19°C。学生被问到“哪两个连续日之间温度上升最多？”计算差值：周一至周二+2，周二至周三-3，周三至周四+4，周四至周五+3，周五至周六+2，周六至周日-1。最大增幅为周三与周四之间的+4°C。另一部分要求描述总体趋势。这一周总体呈上升趋势，尽管末尾略有下降。切勿将折线图与条形图混淆；折线图展示随时间的变化。

---

7. Probability Scale and Simple Probability | 概率的度量与简单概率

Question 7 covered the probability scale from 0 to 1 and basic probability language. One task was to mark the probability of an event on a scale. For example, ‘It will snow in the Sahara Desert’ is impossible, so its probability is 0. ‘A fair coin landing on heads’ has a probability of 0.5, marked exactly halfway along the scale. Students then had to find the probability of drawing a red card from a standard 52-card deck. There are 26 red cards, so P(red) = 26/52 = 1/2. Probability can be expressed as a fraction, decimal or percentage, but in WJEC answers, fractions in simplest form are often expected. Remember probability = number of favourable outcomes / total number of possible outcomes.

问题7涉及0到1的概率度量和基本的概率语言。一项任务是在刻度上标记某事件的概率。例如，“撒哈拉沙漠会下雪”是不可能的，因此其概率为0。“抛一枚均匀硬币正面朝上”的概率为0.5，标记在刻度正中间。接着学生需要求出从一副标准52张扑克牌中抽到红色牌的概率。有26张红色牌，所以P(红) = 26/52 = 1/2。概率可用分数、小数或百分数表示，但在WJEC的答案中，通常要求使用最简分数。记住概率 = 有利结果数 / 可能结果总数。

---

8. Experimental Probability and Expected Outcomes | 实验概率与预期结果

Question 8 presented a scenario: A spinner has three colours, red, blue and green. After 50 spins, red appeared 22 times, blue 18 times and green 10 times. Students had to calculate the experimental probability of landing on green as 10/50 = 1/5. Using this probability, they needed to predict the number of times green would appear in 300 spins: expected frequency = probability × number of trials = 1/5 × 300 = 60. The question reminded that experimental probability is based on actual results, while theoretical probability assumes fairness. As the number of trials increases, experimental probability should get closer to theoretical probability.

问题8呈现了一个情景：一个转盘有三种颜色，红、蓝、绿。在50次转动后，红色出现22次，蓝色18次，绿色10次。学生需要计算落在绿色的实验概率：10/50 = 1/5。然后利用此概率预测在300次转动中绿色出现的次数：预期频数 = 概率 × 试验次数 = 1/5 × 300 = 60。此题提醒，实验概率基于实际结果，而理论概率假设公平。随着试验次数的增加，实验概率应越来越接近理论概率。

---

9. Two-Way Tables | 双向表

Question 9 used a two-way table to record whether Year 8 pupils are left-handed or right-handed by gender. The completed table was: Boys: Left 4, Right 21, Total 25; Girls: Left 6, Right 19, Total 25; Totals: Left 10, Right 40, Grand Total 50. Students had to fill in missing values and answer questions like, ‘What fraction of pupils are left-handed girls?’ 6 out of 50, which is 6/50 = 3/25. Another question: ‘Are boys more likely to be left-handed than girls?’ Comparing probabilities: P(left|boy) = 4/25 = 0.16, P(left|girl) = 6/25 = 0.24, so girls have a slightly higher chance. Two-way tables are powerful for organizing bivariate categorical data; always check row and column totals add up.

问题9使用一张双向表记录8年级学生按性别的左撇子或右撇子情况。完成的表格为：男生：左撇子4人，右撇子21人，合计25人；女生：左撇子6人，右撇子19人，合计25人；总计：左撇子10人，右撇子40人，总计50人。学生需要填入缺失值并回答诸如“左撇子女生占全体学生的几分之几？”等问题。50人中有6人，即6/50 = 3/25。另一个问题：“男生比女生更容易成为左撇子吗？”比较概率：P(左|男) = 4/25 = 0.16, P(左|女) = 6/25 = 0.24，因此女生概率稍高。双向表是整理双变量分类数据的有效工具；务必检查行和列的合计是否加总正确。

---

10. Comparing Data Sets Using Averages and Range | 利用平均数和极差比较数据集

Question 10 compared the quiz scores of two groups: Group A: 4, 6, 8, 10, 12 and Group B: 5, 5, 8, 11, 11. The mean for Group A is (4+6+8+10+12)/5 = 40/5 = 8. For Group B: (5+5+8+11+11)/5 = 40/5 = 8. Both groups have the same mean, but are the distributions identical? No. To compare consistency, calculate the range: Group A range = 12−4 = 8; Group B range = 11−5 = 6. Group B has a smaller range, so its scores are more consistent. You could also use the median (both 8) or mode (no mode for A, multimodal for B). Always use at least two measures to fully compare data sets.

问题10比较了两组学生的测验得分：A组：4, 6, 8, 10, 12；B组：5, 5, 8, 11, 11。A组的平均数为 (4+6+8+10+12)/5 = 40/5 = 8。B组的平均数为 (5+5+8+11+11)/5 = 40/5 = 8。两组平均数相同，但分布一样吗？不一样。为比较一致性，计算极差：A组极差 = 12−4 = 8；B组极差 = 11−5 = 6。B组极差较小，因此其分数更一致。你还可以使用中位数（两组均为8）或众数（A组没有众数，B组是双众数）。务必使用至少两种度量来全面比较数据集。

---

11. Critical Evaluation of Statistical Diagrams | 统计图表的批判性评估

The final question in many WJEC tests asks students to critique a given statistical graph, such as a bar chart with a truncated vertical axis or a pie chart with percentages that do not sum to 100%. In this mock, a bar chart compared the number of goals scored by two football players, but the vertical axis started at 10 instead of 0, making a small difference look exaggerated. A good answer would state: ‘The axis does not start at zero, so the difference appears larger than it actually is. The chart is misleading.’ Always suggest an improvement, such as redrawing the chart with a full axis starting at zero.

在许多WJEC测试中最后一题要求学生批判给定的统计图表，例如纵轴被截断的条形图或百分比总和不等于100%的饼图。在此次模拟卷中，一张条形图比较了两名足球运动员的进球数，但纵轴从10开始而非0，使得原本较小的差距看起来被夸大。一个出色的回答应指出：“纵轴并非从零开始，因此差距显得比实际更大。图表具有误导性。”始终要提出改进建议，例如以从零开始的完整坐标轴重新绘制图表。

---

12. Key Revision Takeaways for Your Unit Test | 单元测试复习要点总结

To succeed in your Year 8 WJEC Statistics test, practise calculating averages from both lists and frequency tables, drawing and interpreting different chart types, and comparing data using statistical measures. Show all your working clearly, even on simple calculations, because method marks can be awarded. Check that pie chart angles sum to 360°, always label axes, and read questions carefully to decide whether to use theoretical or experimental probability. If you spot a misleading graph, be prepared to explain why it distorts the data. Good luck!

要在8年级WJEC统计测试中取得成功，需要练习从列表和频数表中计算平均数，绘制并解读不同类型的图表，以及利用统计度量比较数据。清晰展示所有计算过程，即使是简单计算，因为可能得到方法分。检查饼图角度总和是否为360°，始终标注坐标轴，并仔细读题以决定使用理论概率还是实验概率。如果你发现误导性图表，准备好解释它为何歪曲了数据。祝你好运！

Published by TutorHao | Statistics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）