Line graphs show how a numerical variable changes as another variable changes, and time-series plots are line graphs where the horizontal axis is time. They are useful because they make patterns visible, such as growth, decline, cycles, sudden changes, and unusual points. Scientists, economists, engineers, and public health researchers use them to compare what happened over days, months, or years.
A clear graph can reveal a story in the data faster than a table of numbers can.
Key Facts
- A line graph connects ordered data points to show change between values.
- In a time-series plot, time belongs on the horizontal axis and the measured variable belongs on the vertical axis.
- Slope between two points = change in y / change in x.
- Percent change = (new value - old value) / old value × 100%.
- A trend is the overall long-term direction of the data, such as increasing, decreasing, or roughly constant.
- A graph can be misleading if the vertical axis is truncated, unevenly scaled, or unlabeled.
Vocabulary
- Line graph
- A graph that displays ordered data points connected by line segments to show how a quantity changes.
- Time series
- A set of data values recorded in time order, usually at regular intervals.
- Trend
- The general long-term pattern or direction in a data set.
- Seasonality
- A repeating pattern in data that occurs at regular time intervals, such as daily, monthly, or yearly cycles.
- Spike
- A sudden, sharp increase in a data value compared with nearby values.
Common Mistakes to Avoid
- Ignoring the axis scale. This is wrong because a steep-looking line may only represent a small change if the vertical scale is compressed or starts far above zero.
- Treating every up and down as an important trend. This is wrong because short-term noise can hide the overall direction of the data.
- Connecting points that are not in correct time order. This is wrong because a time-series plot must follow chronological order to show meaningful change.
- Comparing two lines without checking units and scales. This is wrong because different units, starting values, or axis ranges can make comparisons unfair.
Practice Questions
- 1 A city records average temperatures of 12°C, 15°C, 18°C, 22°C, and 25°C from Monday through Friday. What is the total change in temperature from Monday to Friday, and what is the average change per day over the four intervals?
- 2 A website has 200 visits in January and 260 visits in February. Calculate the percent change from January to February.
- 3 A time-series plot of ice cream sales rises every summer and falls every winter for five years, while the overall yearly average slowly increases. Identify the seasonality and the long-term trend, and explain how both can appear in the same graph.