Reading a data table
A table organizes data into rows and columns. Before reading the numbers, read the headings and units.
| Time (s) | Distance (m) |
|---|---|
| 0 | 0 |
| 2 | 6 |
| 4 | 12 |
| 6 | 18 |
| 8 | 24 |
The independent variable (time) usually goes in the left column. The dependent variable (distance) goes on the right. Here, distance goes up 6 m every 2 seconds, so the object moves at a steady 3 m/s.
Choosing the right graph
A graph turns numbers into a picture so patterns jump out.
| Graph type | Best for | Example |
|---|---|---|
| Line graph | Change over time or continuous data | Temperature through a day |
| Bar graph | Comparing separate categories | Rainfall in different cities |
| Scatter plot | Looking for a relationship between two variables | Height vs. arm span |
| Pie chart | Parts of a whole | Gases in the atmosphere |
| Histogram | How often values fall in ranges | Test scores by range |
Parts of a good graph
- a clear title
- the independent variable on the x-axis, the dependent variable on the y-axis
- axis labels with units
- even scales that fit the data
- a key, if there is more than one data set
Reading trends
A trend is the general direction of the data.
- Positive trend: as x increases, y increases.
- Negative trend: as x increases, y decreases.
- No trend: points are scattered with no pattern.
On a line graph, the slope shows how fast y changes. A steeper line means a faster change. For a distance–time graph, the slope is the speed.
Slope = rise ÷ run = change in y ÷ change in x
For the table above: slope = (24 − 0) m ÷ (8 − 0) s = 3 m/s.
Interpolating and extrapolating
To interpolate is to estimate a value between your data points. At 5 s, the object is probably about 15 m away.
To extrapolate is to extend the trend beyond your data. At 10 s, it might be 30 m away. Extrapolation is riskier, because the pattern might change outside the range you measured.
Scientific models
A model is a simplified representation of something real. Models help us understand things that are too big, too small, too fast or too slow to study directly.
| Type of model | Example |
|---|---|
| Physical model | A globe, a model of the solar system |
| Diagram | The water cycle drawn with arrows |
| Mathematical model | Speed = distance ÷ time |
| Computer model | Weather forecasts, climate simulations |
Every model leaves something out. A globe shows continents but not the rocky layers inside Earth. Good scientists know their model’s limits.
Spotting misleading graphs
- A y-axis that doesn’t start at zero can make small differences look huge.
- Uneven scales distort trends.
- Missing units make graphs meaningless.
Common mistakes
- Switching the axes. The thing you change goes on the x-axis.
- Joining points in a bar graph or using a line graph for categories.
- Extrapolating too far beyond your data.
Try it yourself
Use this data: a cup of hot water cools over time.
| Time (min) | Temperature (°C) |
|---|---|
| 0 | 80 |
| 5 | 62 |
| 10 | 50 |
| 15 | 42 |
| 20 | 37 |
- Which kind of graph should you use?
- Describe the trend.
- Interpolate the temperature at 7.5 minutes.
- Is the line straight or curved? What does that tell you about how fast it cools?
Quick recap
- Read headings and units before reading data.
- Choose the graph type that fits your data.
- Trends show direction; slope shows the rate of change.
- Interpolating stays inside your data; extrapolating goes beyond it.
- Models simplify reality and always have limits.