Year 10 CCEA Statistics: Unit Test Mock Paper Solutions | 单元测试模拟卷解析

📚 Year 10 CCEA Statistics: Unit Test Mock Paper Solutions | 单元测试模拟卷解析

This mock paper is designed to help you review the core topics from the Year 10 CCEA Statistics unit. It includes questions on data handling, charts, averages, measures of spread, scatter graphs, experimental probability, and combined events. Each detailed solution shows the step-by-step thinking you need to achieve full marks in your real test.

这份模拟卷旨在帮助你复习 Year 10 CCEA 统计单元的核心知识点，涵盖数据处理、统计图表、平均值、离散程度、散点图、实验概率和组合事件等题型。每道题的详细解析都展示了完整得分所需的解题思路与步骤。

1. Data Handling and Frequency Tables | 数据处理与频数表

Question 1: Twenty students recorded the number of exercise sessions they completed in a week. The raw data are: 3, 2, 4, 1, 3, 5, 2, 3, 4, 3, 0, 2, 1, 3, 4, 2, 3, 5, 2, 3. Construct a completed frequency table, and find the mode.

题目1： 20 名学生记录了他们一周完成的运动次数，原始数据为：3, 2, 4, 1, 3, 5, 2, 3, 4, 3, 0, 2, 1, 3, 4, 2, 3, 5, 2, 3。请完成频数表，并找出众数。

To create the frequency table, first identify all values ranging from the minimum (0) to the maximum (5). Then use tally marks to count how many times each value appears, ensuring the total frequency adds up to 20.

首先确定最小值为 0，最大值为 5，列出所有可能的数值。然后用画记法统计每个数值出现的次数，确保总频数为 20。

The mode is the value with the highest frequency, which is 3 sessions. It occurs 7 times, more than any other category.

众数是出现次数最多的数值，即 3 次运动，出现了 7 次，远高于其他类别。

2. Bar Charts and Pie Charts | 条形图与饼图

Question 2: Using the frequency table from Question 1, construct a bar chart to display the data. Then calculate the angle needed for each category to draw a pie chart.

题目2： 利用题1的频数表，绘制条形图展示数据，并计算每个类别在饼图中所需的角度。

A bar chart is drawn with the number of sessions on the horizontal axis and frequency on the vertical axis. Bars are of equal width and do not touch, showing the frequency of each discrete value clearly.

绘制条形图时，横轴表示运动次数，纵轴表示频数，条形等宽且彼此分离，清晰呈现每个离散数值的频数。

For a pie chart, the angle for each sector is calculated as: (frequency ÷ total frequency) × 360°. The total frequency is 20.

饼图中每个扇形的角度计算公式为： （该类频数 ÷ 总频数） × 360°。总频数为 20。

Check that the angles sum to 360° (18+36+90+126+54+36 = 360). A protractor is used to draw the sectors accurately.

检查所有角度之和为 360°（18+36+90+126+54+36=360），使用量角器即可准确绘制扇形。

3. Mean, Median and Mode | 平均数、中位数和众数

Question 3: Ten students earned the following marks in a mathematics test: 12, 15, 10, 18, 14, 16, 11, 13, 17, 14. Calculate the mean, median and mode. State which average best represents the data.

题目3： 10 名学生在一次数学测验中的得分为：12, 15, 10, 18, 14, 16, 11, 13, 17, 14。计算平均数、中位数和众数，并指出哪种平均数最能代表这组数据。

First, sort the data in ascending order: 10, 11, 12, 13, 14, 14, 15, 16, 17, 18. The mean is the sum of all values divided by 10.

首先将数据从小到大排序：10, 11, 12, 13, 14, 14, 15, 16, 17, 18。平均数等于所有数据之和除以 10。

Sum = 10+11+12+13+14+14+15+16+17+18 = 140
Mean = 140 ÷