A.6 · Data Collection and Graphing

Rates, percentages and means

Compare counts and rates, calculate the percentage of independent correct responses, and find a mean latency. Worked examples show how the question, denominator and units shape each summary.

Task A.6: Calculate and summarize data in different ways

Useful foundations: A.1: Continuous measurement

The rule

Choose the calculation that matches the question, and state what the numerator, denominator and unit represent.

A larger count can come from a longer observation. A percentage needs a defined set of opportunities. A mean summarizes the values; inspect the individual values to assess their spread.

Key terms
Denominator
The total opportunities, time or number of measurements used as the divisor.
Rate
Number of occurrences divided by observation time, with a stated time unit.

What to look for

DistinctionLook forHow to decide
Count and rateOccurrences, with or without elapsed timeRate = count ÷ observation time.
PercentageA qualifying subset of eligible opportunitiesSubset ÷ total eligible opportunities × 100.
MeanSeveral measurements of the same kindAdd the values and divide by their number.

Worked examples

Rate

Compare unequal observation periods

Mila makes 9 requests during a 3-minute observation and 18 requests during a 9-minute observation. Every request meeting the definition is counted. The question asks which observation has the higher rate per minute.

Relevant facts

  • The observation lengths differ.
  • The same response definition is used.

The first observation has the higher rate.

9 ÷ 3 = 3 per minute; 18 ÷ 9 = 2 per minute

The second observation has more requests in total and fewer requests per minute. Compare the two rates using the same units.

Percentage

Keep prompted responses out of the numerator

Across 15 eligible opportunities, a learner responds correctly without a prompt on 9, correctly after a prompt on 4, and does not respond on 2. The measure is percentage of opportunities with an independent correct response.

Relevant facts

  • All 15 opportunities belong in the denominator.
  • Only 9 qualify as independent correct.

Record 60% independent correct.

9 ÷ 15 × 100 = 60%

Use the 9 independent correct responses as the numerator and all 15 eligible opportunities as the denominator. The four prompted responses and two opportunities with no response remain part of the opportunity count.

Mean

Summarize three latencies

Three measured latencies are 12, 15 and 9 seconds. Each begins at the same defined cue and ends at the same defined response.

Relevant facts

  • There are three measurements in seconds.
  • Their sum is 36 seconds.

Mean latency is 12 seconds.

(12 + 15 + 9) ÷ 3 = 12 seconds

The mean is neither the total time nor evidence that every response began after exactly 12 seconds.

What changes the answer?

Use the two request observations again.

  • First: 9 in 3 minutes. Second: 18 in 9 minutes.

Which has more requests in total?

The second: 18.

The question asks for frequency.

Which has more requests per minute?

The first: 3 per minute.

The question asks for rate.

The requested measure changes the answer even though the data stay fixed.

Remember

  • Write the unit beside the answer.
  • Check who or what belongs in the denominator before calculating.
Sources for this topic

Reviewed 2026-09-30 · A.6 version 3.