Protocol
Build an overall rate from totals
Averaging the printed rates may average the wrong things.
When it fits
- You are combining speeds, throughput rates or other quantities measured per unit of exposure.
When to avoid it
- Stops, idle time and excluded intervals must be treated consistently with the question.
Why it matters
Return to the total quantity and the total time, distance or other denominator. Calculate the overall rate from those totals. The weighting follows the physical question, not the number of rows in the table.
Steps
- Name the quantity and denominator in the rate.
- Recover or obtain the totals for the entire interval.
- Divide once, then compare with any proposed average of component rates.
An example
Traveling 60 km at 30 km/h and 60 km at 60 km/h takes three hours for 120 km: the overall speed is 40 km/h, not 45.
Check your result
The combined rate reproduces the actual total quantity over total exposure.
Keep this limit in mind
- Stops, idle time and excluded intervals must be treated consistently with the question.
Evidence and sources
Supports
An overall rate is calculated from the relevant total quantity divided by total exposure, such as distance divided by time.
An unweighted average of component rates is appropriate only when its weighting matches the actual question.
Chemistry 2e, 1.4: Measurements · Derived quantities and units; independent rate derivation