Year 7 CAIE Statistics: Mock Exam Paper Walkthrough | 7年级CAIE统计：单元测试模拟卷解析

📚 Year 7 CAIE Statistics: Mock Exam Paper Walkthrough | 7年级CAIE统计：单元测试模拟卷解析

This walkthrough is designed to help Year 7 students prepare for their CAIE Statistics unit test. We work through a full mock paper, question by question, covering data collection, charts, averages, spread, probability, and graph interpretation. Each section provides clear explanations, step-by-step solutions, and useful tips. By the end, you will feel confident tackling similar problems in your actual exam.

这套模拟卷解析专为7年级学生准备CAIE统计单元测试而设计。我们逐题讲解一份完整的模拟试卷，涵盖数据收集、图表、平均数、离散程度、概率以及图表解读。每节都提供了清晰的解释、分步解答和实用技巧。学完本文后，你将自信应对实际考试中的类似题目。

1. Data Collection, Tally Charts, and Frequency Tables | 数据收集、记数表与频数表

A survey asked 20 students to name their favourite fruit. The raw data collected is: Apple, Banana, Apple, Orange, Banana, Apple, Banana, Apple, Orange, Banana, Apple, Banana, Apple, Banana, Orange, Apple, Banana, Apple, Orange, Banana. To make sense of this list, we organise it using a tally chart and then a frequency table.

一项调查询问了20名学生他们最喜欢的水果。收集到的原始数据如下：苹果、香蕉、苹果、橙子、香蕉、苹果、香蕉、苹果、橙子、香蕉、苹果、香蕉、苹果、香蕉、橙子、苹果、香蕉、苹果、橙子、香蕉。为了理解这串数据，我们使用记数表进行整理，然后制作频数表。

Solution Steps:

解答步骤：

Step 1: Identify categories. The possible responses are Apple, Banana, and Orange. Write these as headings in the tally chart.

步骤1：确定类别。 可能的回答有苹果、香蕉和橙子。将这些作为记数表的标题。

Step 2: Tally each response. Go through the list one by one. For the first ‘Apple’, draw one vertical line in the tally column next to Apple. Continue this way, making a group of five tally marks (four vertical lines crossed with a diagonal slash) each time you reach five. After finishing, the tallies for Apple should show two full groups of five, Banana shows one group of five plus two, and Orange shows three individual marks.

步骤2：逐条记录。 逐一浏览列表。第一个“苹果”就在苹果旁边的记数列画一条竖线。如此继续，每满五条记数标记（四条竖线加一条斜线）就形成一组。完成后，苹果的记数应显示完整的两组五条，香蕉显示一组五条加两条，橙子显示三条单独的标记。

Step 3: Count frequencies. From the tally marks, count how many times each fruit appears. Apple: 10, Banana: 7, Orange: 3. Record these numbers in the frequency column. The total frequency is 10+7+3=20, which matches the number of students.

步骤3：数出频数。 根据记数标记，数出每种水果出现的次数。苹果：10，香蕉：7，橙子：3。将这些数字填入频数列。频数总和为10+7+3=20，与学生人数一致。

The completed frequency table looks like this:

完成的频数表如下：

Fruit	Tally	Frequency
Apple	卌卌	10
Banana	卌 \|\|	7
Orange	\|\|\|	3
Total		20

Always check that the total frequency equals the number of data items originally collected.

务必检查频数总和是否等于最初收集的数据项数量。

2. Bar Charts | 条形图

A bar chart is used to display the frequencies from the frequency table visually. Each category is represented by a rectangular bar whose height shows its frequency. The bars must be of equal width and equally spaced, and the chart needs a title and labeled axes.

条形图用于直观显示频数表中的频数。每个类别用一个矩形条表示，其高度代表频数。条形宽度必须相等、间距均匀，图表要有标题和带标签的轴。

Here is the mock question: ‘Draw a bar chart to represent the fruit frequency data.’ Let’s go through the construction.

下面是模拟题：“画一个条形图来表示水果频数数据。”我们来一步一步画。

Step 1: Draw and label the axes. The horizontal axis (x‑axis) shows the fruit categories: Apple, Banana, Orange. The vertical axis (y‑axis) shows the frequency. Choose a scale that goes up to at least the highest frequency (10). A scale of 1 square = 1 unit works well here.

步骤1：画出并标记轴。 横轴（x轴）表示水果类别：苹果、香蕉、橙子。纵轴（y轴）表示频数。选择一个刻度，最高至少要到最大频数（10）。此处用1格=1单位的刻度合适。

Step 2: Draw the bars. For Apple, draw a bar up to 10 on the y‑axis. For Banana, up to 7. For Orange, up to 3. All bars have the same width and do not touch each other.

步骤2：画出条形。 苹果对应画到纵轴10的高度；香蕉画到7；橙子画到3。所有条形宽度相同且彼此不接触。

Step 3: Add a title. Give the chart a clear title, such as ‘Favourite Fruit of 20 Students’.

步骤3：添加标题。 给图表起一个清晰的标题，例如“20名学生最喜欢的水果”。

The bar chart should clearly show that Apple is the most popular fruit, followed by Banana, then Orange.

条形图应清楚显示苹果最受欢迎，其次是香蕉，然后是橙子。

3. Pictograms | 象形图

A pictogram uses symbols or pictures to represent data. Each symbol can stand for a certain number of items. In this mock question, we use a smiley face ☺ to represent 2 students. Construct a pictogram for the fruit data.

象形图用符号或图片来表示数据。每个符号可以代表一定数量的项目。在这道模拟题中，我们用一个笑脸☺代表2名学生。请为水果数据制作一个象形图。

Step 1: Determine the number of symbols for each category. Divide each frequency by 2 (since 1 ☺ = 2 students). Apple: 10 ÷ 2 = 5 smileys. Banana: 7 ÷ 2 = 3.5 → we need 3 full smileys and a half smiley to represent 1 student. Orange: 3 ÷ 2 = 1.5 → 1 full smiley and a half smiley.

步骤1：确定每个类别的符号数量。 将每个频数除以2（因为1个☺=2名学生）。苹果：10÷2=5个笑脸。香蕉：7÷2=3.5→需要3个完整笑脸和一个半笑脸代表1名学生。橙子：3÷2=1.5→1个完整笑脸和一个半笑脸。

Step 2: Draw the pictogram. Align the symbols in rows next to the fruit names. The half smiley is drawn as half of the smiley face. Remember to include a key: e.g., ‘☺ = 2 students’.

步骤2：绘制象形图。 将符号在水果名称旁边排成一行。半笑脸绘制成笑脸的一半。记得加上图例，例如“☺ = 2名学生”。

Step 3: Check totals. Apple: 5×2=10; Banana: 3×2+1=7; Orange: 1×2+1=3. This confirms the pictogram is correct.

步骤3：检查总数。 苹果：5×2=10；香蕉：3×2+1=7；橙子：1×2+1=3。这确认了象形图正确无误。

4. Pie Charts | 饼图

A pie chart shows proportions by dividing a circle into sectors. The angle of each sector is calculated using the formula:

Angle = (Frequency ÷ Total frequency) × 360°

饼图通过将圆分成扇形来显示比例。每个扇形的角度用以下公式计算：

角度 = (频数 ÷ 总频数) × 360°

Using the fruit data: Total frequency = 20.

使用水果数据：总频数 = 20。

Apple: (10 ÷ 20) × 360° = 0.5 × 360° = 180°
Banana: (7 ÷ 20) × 360° = 0.35 × 360° = 126°
Orange: (3 ÷ 20) × 360° = 0.15 × 360° = 54°

苹果：(10 ÷ 20) × 360° = 0.5 × 360° = 180°
香蕉：(7 ÷ 20) × 360° = 0.35 × 360° = 126°
橙子：(3 ÷ 20) × 360° = 0.15 × 360° = 54°

Check that the angles add up to 360°: 180°+126°+54° = 360°. Then draw the circle and use a protractor to mark the angles. Label each sector with the fruit name and percentage or frequency. The largest sector represents Apple, the most popular fruit.

检查角度总和是否为360°：180°+126°+54° = 360°。然后画圆，用量角器标出角度。每个扇区标上水果名称以及百分比或频数。最大的扇区代表苹果，最受欢迎的水果。

5. Mean, Median, and Mode | 平均数、中位数与众数

This mock question presents the ages of seven children at a party: 12, 15, 13, 12, 18, 12, 10. Find the mean, median, and mode.

这道模拟题给出派对上七个孩子的年龄：12, 15, 13, 12, 18, 12, 10。请计算平均数、中位数和众数。

Mean: Add all values: 12+15+13+12+18+12+10 = 92. Divide by 7: 92 ÷ 7 ≈ 13.14 (to 2 decimal places).

Mean = 92 ÷ 7 ≈ 13.14

平均数： 将所有数值相加：12+15+13+12+18+12+10 = 92。除以7：92 ÷ 7 ≈ 13.14（保留两位小数）。

Median: First, order the numbers from smallest to largest: 10, 12, 12, 12, 13, 15, 18. The median is the middle value. Since there are 7 numbers, the 4th value is the median: 12.

中位数： 首先将数字从小到大排序：10, 12, 12, 12, 13, 15, 18。中位数是中间的值。因为有7个数字，第4个值就是中位数：12。

Mode: The mode is the number that appears most often. Here, 12 appears three times, while all others appear once. Thus, the mode is 12.

众数： 众数是出现次数最多的数字。这里12出现了三次，其他数字只出现一次。所以众数是12。

Remember: The mean gives the average, the median shows the middle, and the mode indicates the most frequent value.

记住：平均数给出平均值，中位数表示中间值，众数指出最常见的数值。

6. Range | 极差

The range measures how spread out the data is. It is the difference between the largest and smallest values.

Range = Maximum – Minimum

极差衡量数据的分散程度。它是最大值与最小值之差。

极差 = 最大值 – 最小值

Using the same ages (10, 12, 12, 12, 13, 15, 18), the maximum is 18 and the minimum is 10. So the range = 18 – 10 = 8. A small range means the data values are close together; a large range shows they are more spread out.

使用同样的年龄数据（10, 12, 12, 12, 13, 15, 18），最大值为18，最小值为10。因此极差 = 18 – 10 = 8。极差小说明数据值比较集中；极差大表明它们分散得较开。

Always think about outliers. If an age of 45 were added, the range would become much larger, showing that one extreme value can greatly affect the range.

始终考虑异常值。如果加入一个45岁的年龄，极差会变得大得多，这表明一个极值能大幅影响极差。

7. Introduction to Probability | 概率入门

Probability tells us how likely an event is to happen. We find it by dividing the number of favourable outcomes by the total number of possible outcomes.

Probability = Favourable outcomes ÷ Total outcomes

Published by TutorHao | Year 7 统计 Revision Series | aleveler.com

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Year 7 CAIE Statistics: Mock Exam Paper Walkthrough | 7年级CAIE统计：单元测试模拟卷解析