📚 Line Graphs and Data Interpretation | 折线图与数据解读
Line graphs are a key part of IGCSE mathematical statistics. They show how one variable changes in relation to another, usually over time. This article covers reading, plotting, and comparing line graphs so you can handle data questions with confidence.
折线图是 IGCSE 数学统计部分的重要内容。它表示一个变量随另一个变量（通常是时间）变化的情况。本文涵盖折线图的读取、绘制和比较，帮助你自信应对数据题。
1. What Is a Line Graph? | 什么是折线图？
A line graph consists of plotted points connected by straight line segments. The horizontal axis (x-axis) is often time, distance, or another ordered category; the vertical axis (y-axis) shows the value being measured.
折线图由已描出的点用直线段连接而成。水平轴（x 轴）通常表示时间、距离或其他有序类别；垂直轴（y 轴）表示被测量的值。
Common examples include temperature over a day, height over several months, sales over a week, and distance travelled over a journey.
常见例子包括一天内的温度变化、几个月内的身高变化、一周内的销售额，以及旅途中的距离变化。
2. Reading Values from a Line Graph | 从折线图中读取数值
To read a value, move vertically from a point on the x-axis until you hit the line, then move horizontally to the y-axis. If the point lies between gridlines, give a sensible estimate.
读取数值时，从 x 轴上的点垂直向上找到折线上的点，再水平看向 y 轴。如果点位于网格线之间，则给出合理的估计值。
Consider this data set showing temperature over five hours:
考虑以下显示五小时内温度变化的数据：
| Time (h) | 0 | 1 | 2 | 3 | 4 | 5 |
| Temperature (°C) | 12 | 15 | 18 | 17 | 22 | 25 |
From the graph, the temperature at 2 hours is exactly 18°C. If a point lies halfway between 18°C and 20°C, you can estimate it as 19°C.
从图中可以看出，2 小时时的温度正好是 18°C。如果某个点位于 18°C 和 20°C 的中间，你可以估计其为 19°C。
3. Choosing a Suitable Scale | 选择合适的刻度
The scale must cover the highest and lowest data values. Equal intervals should be used, such as 0, 5, 10, 15, 20. A broken scale or uneven jumps can make differences look larger or smaller than they really are.
刻度必须覆盖数据的最高值和最低值。应使用相等的间隔，例如 0、5、10、15、20。断开的刻度或不等距的跳跃会使差异看起来比实际更大或更小。
Always label both axes with the variable name and its unit, such as 'Time (minutes)' or 'Distance (km)'.
务必在两个坐标轴上标出变量名称和单位，例如 '时间（分钟）' 或 '距离（公里）'。
4. Plotting a Line Graph Step by Step | 逐步绘制折线图
Follow these steps when you draw a line graph from a data table:
从数据表绘制折线图时，请按照以下步骤操作：
First, label the x-axis and y-axis with the variable names and units. Second, choose a suitable scale for each axis so that all points fit. Third, plot each data pair as a clear point. Fourth, join consecutive points with straight line segments using a ruler.
首先，用变量名称和单位标注 x 轴和 y 轴。其次，为每个坐标轴选择合适的刻度，使所有点都能容纳。第三，将每一组数据描成清晰的数据点。第四，用直尺按顺序用直线段连接相邻的点。
Do not extend the line beyond the first and last data points unless you are making a prediction and the question asks for it.
除非题目要求进行预测，否则不要将折线延伸到第一个和最后一个数据点之外。
5. Interpreting Trends | 解读变化趋势
A rising line shows an increase; a falling line shows a decrease; a flat line shows no change. The steeper the line, the faster the change. Use precise words such as 'peak', 'levelled off', 'rose steadily', and 'fell sharply'.
上升的折线表示增加；下降的折线表示减少；水平的折线表示不变。折线越陡，变化越快。使用准确的词语，例如 '峰值'、'趋于平稳'、'稳步上升' 和 '急剧下降'。
On a distance–time graph, the gradient of the line represents speed. A steeper gradient means a higher speed.
在距离–时间图中，折线的斜率表示速度。斜率越大表示速度越快。
Speed = Δdistance ÷ Δtime
6. Comparing Two Line Graphs | 比较两条折线图
When two line graphs share the same axes, compare their gradients and turning points. A higher line at a given x-value means a larger y-value. A steeper graph means a greater rate of change.
当两条折线在同一坐标系中时，比较它们的斜率和转折点。在某个 x 值处，较高的折线表示 y 值较大。较陡的折线表示变化率较大。
If one line is above another for the whole graph, it has a greater value throughout that interval. If two lines cross, the crossover point shows where the two quantities become equal.
如果一条折线在整个区间内位于另一条折线上方，则表示在该区间内它的数值始终更大。如果两条折线相交，交点表示两个量相等的位置。
7. Common Errors and Misleading Graphs | 常见错误与误导性图表
Common errors include using uneven intervals, starting the y-axis at a non-zero value without a break symbol, forgetting axis labels, and joining points that should not be connected.
常见错误包括使用不均匀的间隔、y 轴不从零开始且没有断开符号、忘记标注坐标轴，以及连接了不应连接的点。
A misleading line graph can exaggerate a small change by using a very narrow y-axis range. Always check the scale before drawing a conclusion.
误导性折线图可能通过使用非常窄的 y 轴范围来夸大小幅变化。在得出结论之前，务必检查刻度。
8. Exam-Style Practice | 考试类型练习
The table shows a cyclist's distance from home. Plot a line graph and determine the fastest average speed.
下表显示一名骑车人离家的距离。绘制折线图并确定最快的平均速度。
| Time (min) | 0 | 5 | 10 | 15 | 20 | 25 |
| Distance (km) | 0 | 2.5 | 5 | 7 | 11 | 14 |
The steepest segment is between 15 and 20 minutes. The average speed over that interval is calculated as:
最陡的线段在 15
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