Trend measurement
What does rate of change measure?
Rate of change describes how much a measured quantity changes for each unit change in another variable, such as time, distance, temperature, or concentration.
Formula
Average rate of change formula
Average rate of change(final value − initial value) ÷ (final independent value − initial independent value)
Worked example
Temperature increases from 20 to 35 in 5 minutes
- Change in temperature: 35 − 20 = 15.
- Change in time: 5 − 0 = 5.
- Average rate of change: 15 ÷ 5 = 3 units per minute.
- Percentage change: 15 ÷ 20 × 100 = 75%.
Direction
Interpret positive, negative, and zero rates
Positive rate
Increasing trend
The measured value rises across the selected interval.
Negative rate
Decreasing trend
The measured value falls across the selected interval.
A rate of zero means the measured value did not change across the interval.
Units
Report both variable units
A rate should be reported as the measured variable unit per independent-variable unit, such as degrees Celsius per minute, centimeters per second, or grams per hour.
Relative change
Percentage change formula
Percentage change(final value − initial value) ÷ |initial value| × 100%
Percentage change is undefined when the initial value is zero because division by zero is not possible.
Limitations
Average rate can hide variation
- It summarizes only the selected start and end points.
- It may hide changes that occurred within the interval.
- A graph should be inspected for curvature, plateaus, and anomalies.
- Units and experimental context must be stated clearly.
Questions and answers
Rate of change FAQ
What is average rate of change?
Average rate of change is the change in the measured value divided by the change in the corresponding independent variable.
Is average rate of change the same as slope?
Between two points, average rate of change is the slope of the secant line connecting those points.
How is percentage change calculated?
Percentage change equals final value minus initial value, divided by the absolute initial value, multiplied by 100 percent.
Why is percentage change undefined when the initial value is zero?
Percentage change requires division by the initial value, so it is undefined when the initial value equals zero.