📚 Year 7 Edexcel Statistics: Unit Test Practice Paper Walkthrough | 七年级爱德思统计：单元测试模拟卷解析
Welcome to this detailed walkthrough of a typical Year 7 Edexcel Statistics unit test. We will guide you through ten common question types, showing you step-by-step how to read data, draw accurate charts, calculate averages and range, and avoid common mistakes. Each section presents a sample question, followed by a clear method and full solution, so you can build confidence and master the key skills assessed in your exam.
欢迎来到这份典型的七年级爱德思统计单元测试的详细解析。我们将带你走完十种常见题型，逐步展示如何读取数据、绘制准确的图表、计算平均数和极差，以及如何避免常见错误。每个小节都提供一道样题，然后给出清晰的方法和完整解答，帮助你建立信心、掌握考试中考查的核心技能。
1. Question 1: Tally Charts and Frequency Tables | 问题1：计数表与频数表
A class recorded the number of books read by each student during the holiday. The teacher noted the results using tally marks: Anna IIII, Ben IIII II, Chloe I, David IIII III, Eva II, Freddie IIII, Grace IIII I. The first task is to complete a frequency table and find the total number of books read.
一个班级记录了每个学生在假期里阅读的书籍数量。老师用计数符号记下了结果：Anna IIII, Ben IIII II, Chloe I, David IIII III, Eva II, Freddie IIII, Grace IIII I。第一个任务是完成频数表并求出阅读的总书籍数。
Step 1: Count each group of tallies carefully. Remember that every group of five is shown as four vertical lines and one diagonal line crossing them. For Ben, IIII II represents 5 + 2 = 7 books. For Chloe, one tally means 1 book. Fill in the frequency column: Anna 4, Ben 7, Chloe 1, David 8, Eva 2, Freddie 5, Grace 6.
第一步：仔细数出每一组计数符号。记住，每五个一组用四条竖线和一条斜线交叉表示。Ben的 IIII II 代表 5+2=7 本书。Chloe的一条线表示1本。在频数列填入：Anna 4，Ben 7，Chloe 1，David 8，Eva 2，Freddie 5，Grace 6。
Step 2: To find the total number of books, add all the frequencies: 4 + 7 + 1 + 8 + 2 + 5 + 6 = 33. So, the class read 33 books in total.
第二步：要求总书籍数，把所有频数相加：4 + 7 + 1 + 8 + 2 + 5 + 6 = 33。因此全班总共阅读了33本书。
Key point: Never confuse the tally marks with the frequency itself. A tally of IIII III is not just ‘III’; it counts as 8. Always convert tallies into numbers before any further calculations.
关键点：不要混淆计数符号和频数本身。IIII III 这样的计数不是简单地看作几个 I，而是代表 8。进行进一步计算之前，一定要先将计数符号转换成数字。
2. Question 2: Drawing a Bar Chart | 问题2：绘制条形图
Using the same data on books read, the next question asks you to draw a bar chart to represent the information. The categories are the students’ names, and the height of each bar must match the frequency.
利用相同的阅读数据，下一道题要求你画一幅条形图来表示这些信息。横轴类别是学生的名字，每个条形的高度必须与频数对应。
Step 1: Draw two axes with a ruler. Label the horizontal axis ‘Student’ and the vertical axis ‘Number of books read’. Choose a scale for the vertical axis that can reach the maximum value of 8. A sensible scale would be going up in 1s or 2s, from 0 to 8 or 10.
第一步：用尺子画出两条坐标轴。横轴标注 ‘Student’，纵轴标注 ‘Number of books read’。为纵轴选择一个能涵盖最大数值8的刻度。合理的刻度可以是按1或2递增，从0到8或10。
Step 2: Draw bars of equal width for each student. The bar for Anna should reach 4, Ben’s bar to 7, Chloe’s to 1, and so on. Leave equal gaps between bars. Do not forget to add a title, such as ‘Books read by students during holiday’.
第二步：为每个学生画出宽度相同的条形。Anna 的条高应为4，Ben 的条高为7，Chloe 的条高为1，以此类推。条形之间留出相等的间距。别忘了加上标题，例如 ‘Books read by students during holiday’。
Common mistake: Many students forget to label the axes or start the vertical axis from a number other than zero. Always start at 0, otherwise the differences between categories can look exaggerated and misleading.
常见错误：很多学生忘记标注坐标轴，或者纵轴不从零开始。一定要从零开始，否则类别之间的差异会看起来被夸大，从而产生误导。
3. Question 3: Pictograms | 问题3：象形图
A pictogram uses symbols to show data. In a sample question, the number of ice creams sold each day is shown: Monday 20, Tuesday 15, Wednesday 25, Thursday 10, Friday 30. The key tells you that one ice cream symbol represents 5 ice creams. You must draw the pictogram and answer questions like ‘How many more were sold on Friday than Tuesday?’
象形图使用符号来表示数据。在一道样题中，每天售出的冰淇淋数量如下：星期一20，星期二15，星期三25，星期四10，星期五30。图例告诉你一个冰淇淋符号代表5个冰淇淋。你必须画出象形图，并回答诸如 ‘星期五比星期二多卖了多少个？’ 这类问题。
Step 1: Work out how many symbols are needed for each day by dividing the number of ice creams by 5. Monday: 20 ÷ 5 = 4 full symbols. Tuesday: 15 ÷ 5 = 3 symbols. Wednesday: 5 symbols. Thursday: 2 symbols. Friday: 6 symbols.
第一步：用冰淇淋数除以5，算出每天需要多少个符号。星期一：20 ÷ 5 = 4 个完整符号。星期二：15 ÷ 5 = 3 个。星期三：5 个。星期四：2 个。星期五：6 个。
Step 2: Draw the symbols neatly in rows, using part of a symbol for remainders if needed. Here there are no remainders. To find the difference between Friday and Tuesday: 30 – 15 = 15 ice creams, which is also shown by 3 more symbols.
第二步：整齐地按行画出符号，若有余数可使用符号的一部分。这里没有余数。计算星期五与星期二的差值：30 – 15 = 15 个冰淇淋，也就是多了3个符号。
Top tip: Always check the key. If the symbol represents 2, 5 or 10, the division step is crucial. Many pupils lose marks by simply drawing the number they see without dividing.
高分提示：一定要检查图例。如果每个符号代表2、5或10，除法步骤至关重要。许多学生因为直接把看到的数字当符号数量画出来而失分。
4. Question 4: Mode and Median | 问题4：众数和中位数
A question provides this list of the number of pets owned by 10 children: 0, 1, 2, 1, 3, 0, 2, 1, 4, 2. You are asked to find the mode and the median. The mode is the most frequent value, and the median is the middle value when the data is ordered.
一道题目给出了10个孩子拥有宠物数量的列表：0, 1, 2, 1, 3, 0, 2, 1, 4, 2。要求你找出众数和中位数。众数是最常出现的数值，中位数则是将数据排序后位于中间的值。
Step 1: To find the mode, tally the frequency of each number: 0 appears twice, 1 appears three times, 2 appears three times, 3 appears once, 4 appears once. The highest frequency is 3, which occurs for both 1 and 2. So the data set is bimodal, with modes 1 and 2.
第一步：为求众数，统计每个数字出现的频数：0出现2次，1出现3次，2出现3次，3出现1次，4出现1次。最高频数是3，对应数值1和2。因此这组数据是双众数的，众数为1和2。
Step 2: To find the median, write the numbers in ascending order: 0, 0, 1, 1, 1, 2, 2, 2, 3, 4. Since there are 10 numbers (an even amount), the median is the average of the 5th and 6th values. The 5th is 1 and the 6th is 2. Median = (1 + 2) ÷ 2 = 1.5.
第二步：为求中位数，将数字按升序排列：0, 0, 1, 1, 1, 2, 2, 2, 3, 4。因为有10个数（偶数个），中位数是第5和第6个值的平均数。第5个是1，第6个是2。中位数 = (1 + 2) ÷ 2 = 1.5。
Remember: The median does not have to be one of the actual data values, as shown here. For odd-sized data sets, the median is the exact middle term after ordering.
牢记：中位数不一定是数据中实际出现的值，如此处所示。对于奇数个数据，中位数就是排序后正中间的那个数值。
5. Question 5: Mean and Range | 问题5：均值和极差
From the same pets data, you now need to calculate the mean and the range. The mean is the sum of all values divided by the number of values. The range is the difference between the largest and smallest values.
沿用同一组宠物数据，现在你需要计算均值和极差。均值是所有数值之和除以数值的个数。极差是最大值与最小值之差。
Step 1: Add all the numbers: 0 + 1 + 2 + 1 + 3 + 0 + 2 + 1 + 4 + 2 = 16. There are 10 values, so the mean is 16 ÷ 10 = 1.6. You can express the mean as a decimal, even though we cannot have 1.6 pets in reality.
第一步：把所有数字加起来：0 + 1 + 2 + 1 + 3 + 0 + 2 + 1 + 4 + 2 = 16。一共有10个数值，所以均值是 16 ÷ 10 = 1.6。虽然现实中不可能有1.6只宠物，但均值可以表示为小数。
Step 2: Identify the largest value (4) and the smallest value (0). Range = 4 – 0 = 4. This tells us the spread of the pets data is 4.
第二步：找出最大值（4）和最小值（0）。极差 = 4 – 0 = 4。这说明宠物数据的分布跨度为4。
Common mistake: When calculating the mean, double-check that you have included every number and counted correctly. A common slip is to miscount how many data items there are.
常见错误：计算均值时，要仔细检查是否包含了每个数字并计数正确。常见失误是数错数据项的总数。
6. Question 6: Line Graphs | 问题6：线形图
A science experiment measures the height of a seedling every day for a week. The results are: Day 1: 2 cm, Day 2: 3 cm, Day 3: 5 cm, Day 4: 6 cm, Day 5: 8 cm, Day 6: 11 cm, Day 7: 14 cm. A line graph is the best way to show a trend over time. You need to plot the points and describe the growth.
一项科学实验在一周内每天测量一株幼苗的高度。结果如下：第1天：2 cm，第2天：3 cm，第3天：5 cm，第4天：6 cm，第5天：8 cm，第6天：11 cm，第7天：14 cm。线形图是展示随时间变化趋势的最佳方式。你需要描点并描述生长情况。
Step 1: Draw and label the axes. The horizontal axis is ‘Day’ from 1 to 7. The vertical axis is ‘Height in cm’, with a scale from 0 to at least 14, perhaps stepping by 2. Plot each pair of values with a small cross, then connect the crosses with straight lines.
第一步：画出并标注坐标轴。横轴为 ‘Day’，从1到7。纵轴为 ‘Height in cm’，刻度从0到至少14，可以按2递增。用一个小叉号在图上标出每一对数值，然后用直线将叉号连接起来。
Step 2: Look at the steepness of the line segments. The biggest jump is between Day 6 and Day 7, where the height increased by 3 cm. The overall trend is that the seedling grows steadily but speeds up slightly later. The line graph makes this pattern easy to see immediately.
第二步：观察各段线段的倾斜程度。增长最大的是第6天到第7天之间，高度增加了3厘米。总体趋势是幼苗稳定生长，但后期略有加速。线形图让这种模式一目了然。
In a test, you might be asked: ‘Between which two days was growth the slowest?’ Look for the smallest vertical rise, which is from Day 1 to Day 2 (only 1 cm).
在测试中，你可能会被问到：’哪两天之间的生长最慢？’ 找出垂直上升幅度最小的地方，即第1天到第2天（仅1厘米）。
7. Question 7: Pie Charts | 问题7：饼图
A survey of 30 students asks for their favourite colour. The results are: Red 12, Blue 8, Green 6, Yellow 4. To draw a pie chart, you must calculate the angle for each sector, knowing that a full circle is 360° and represents all 30 students.
一项针对30名学生的调查询问了他们最喜欢的颜色。结果是：红色12人，蓝色8人，绿色6人，黄色4人。要绘制饼图，你必须计算每个扇区的角度，知道整个圆是360°，代表全部30名学生。
Step 1: Find the angle for one student: 360° ÷ 30 = 12° per student. Multiply each frequency by 12: Red = 12 × 12 = 144°, Blue = 8 × 12 = 96°, Green = 6 × 12 = 72°, Yellow = 4 × 12 = 48°. Check that the sum is 360°.
第一步：求每名学生对应的角度：360° ÷ 30 = 12°/人。将每个频数乘以12：红色 = 12 × 12 = 144°，蓝色 = 8 × 12 = 96°，绿色 = 6 × 12 = 72°，黄色 = 4 × 12 = 48°。检查总和是否为360°。
Step 2: Use a protractor to draw the angles accurately. Start from a vertical line and measure each sector. Label each sector with the colour and its frequency. Add a title, such as ‘Favourite colours of 30 students’.
第二步：使用量角器准确画出角度。从一条竖线开始，依次量出每个扇区。为每个扇区标注颜色和频数。加上标题，例如 ‘Favourite colours of 30 students’。
In the exam, you may also be asked what fraction of the students chose Red. That would be 12/30, which simplifies to 2/5. The angle calculation and fraction are closely linked, so check both.
考试中，你可能还会被问到选择红色的学生占几分之几。答案是12/30，化简为2/5。角度计算和分数紧密相关，因此要同时检查。
8. Question 8: Interpreting and Comparing Data | 问题8：数据解读与比较
Two sets of test scores are given: Class A scored 45, 52, 67, 72, 81, 85, 90, 93. Class B scored 50, 55, 60, 68, 70, 75, 80, 88. You are asked to calculate the mean, median and range for each class, and write two sentences comparing them.
给出了两组测试成绩：A班得分为45, 52, 67, 72, 81, 85, 90, 93。B班得分为50, 55, 60, 68, 70, 75, 80, 88。要求你计算每个班的均值、中位数和极差，并用两句话对它们进行比较。
Step 1: For Class A, sum = 45+52+67+72+81+85+90+93 = 585. There are 8 scores, so mean = 585 ÷ 8 = 73.125. To find the median, order is already given; the middle two are 72 and 81, so median = (72+81)÷2 = 76.5. Range = 93 – 45 = 48.
第一步：对于A班，总和 = 45+52+67+72+81+85+90+93 = 585。有8个分数，均值 = 585 ÷ 8 = 73.125。排序已经给出，中间两个是72和81，中位数 = (72+81)÷2 = 76.5。极差 = 93 – 45 = 48。
Step 2: For Class B, sum = 50+55+60+68+70+75+80+88 = 546. Mean = 546 ÷ 8 = 68.25. Median = (68+70)÷2 = 69. Range = 88 – 50 = 38.
第二步：对于B班，总和 = 50+55+60+68+70+75+80+88 = 546。均值 = 546 ÷ 8 = 68.25。中位数 = (68+70)÷2 = 69。极差 = 88 – 50 = 38。
Comparison: Class A has a higher mean (73.1 vs 68.3) and a higher median, so overall they performed better. However, Class A’s range is larger (48 vs 38), which means the scores are more spread out, with a lower minimum. Class B is more consistent.
比较：A班的均值（73.1 对比 68.3）和中位数都更高，因此整体表现更好。然而A班的极差更大（48 对比 38），意味着分数分布更广，最低分也更低。B班则更加整齐一致。
9. Question 9: Spotting Misleading Graphs | 问题9：识别误导性图表
The final section of the test often includes a graph that has been drawn in a misleading way. For example, a bar chart shows four months’ sales: January 100 units, February 110 units, March 105 units, April 115 units. However, the vertical axis starts at 95, not 0, making the February bar look nearly four times taller than January’s.
试卷的最后部分通常包括一幅绘制方式具有误导性的图表。例如，一张条形图显示了四个月的销售额：一月100件，二月110件，三月105件，四月115件。然而，纵轴从95开始而不是0，使得二月的条形看起来比一月的高了近四倍。
Step 1: Identify the trick. The difference between January and February is only 10 units, but because the axis is cut, the visual difference is exaggerated. This could make the viewer think sales have increased dramatically when they have only grown slightly.
第一步：识别出花招。一月与二月之间的差异只有10件，但由于纵轴被截断，视觉差异被夸大了。这使得观众可能以为销售额大幅增长，而实际只略微增长。
Step 2: To correct the graph, the vertical axis should be redrawn starting from 0. Then the bars would differ only slightly in height. Always check the scale and the starting point on any chart you are asked to read or evaluate.
第二步：为修正图表，纵轴应该重新绘制并从0开始。这样条形的高度差异就会很小。在阅读或评价任何图表时，一定要检查刻度的起点。
Another common trick is using uneven intervals on the axis, or pictograms where the symbol size is changed instead of the number of symbols. Always read the labels and key carefully.
另一个常见的误导手法是坐标轴上使用了不均匀的间距，或者在象形图中改变符号的大小而不是改变符号的数量。一定要仔细阅读标签和图例。
10. Question 10: Word Problems and Data Collection | 问题10：文字题与数据收集
A word problem may ask you to plan a statistical investigation. For instance: ‘You want to find out the most popular sport among Year 7 students in your school. Describe how you would collect, record and display the data.’
文字题可能会要求你设计一项统计调查。例如：’你想了解本校七年级学生中最受欢迎的运动。请描述你将如何收集、记录和展示数据。’
Step 1: Decide on the data collection method. A questionnaire or a survey where each student picks one favourite sport would work well. You could use a tally chart to record responses as you ask each student, grouping sports like football, netball, swimming, tennis, athletics and ‘other’.
第一步：决定数据收集方法。采用问卷或者让每个学生选择一项最爱的运动就很有效。你可以用计数表来记录回复，在询问每个学生时划记，把运动分类为足球、英式篮球、游泳、网球、田径和’其他’。
Step 2: After collecting the tallies, convert them into a frequency table. To display the data, a bar chart is an excellent choice because it clearly shows which category has the highest frequency. Alternatively, a pie chart could show the proportions. Finally, you can find the mode to state the most popular sport.
第二步：收集完计数后，将它们转换成频数表。为了展示数据，条形图是极佳的选择，因为它能清晰显示哪个类别的频数最高。或者，也可以使用饼图来展示比例。最后，可以求出众数以说明最受欢迎的运动。
Remember to mention that you need to ask a large enough sample to make the results reliable. In a Year 7 test, they are testing your understanding of the whole statistical cycle: pose a question, collect data, organise and represent it, then interpret the results.
记住要提到，你需要询问足够大的样本以确保结果可靠。在七年级的测试中，他们考查的是你对整个统计循环的理解：提出问题、收集数据、整理和展示数据，然后解读结果。
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