From numbers to a defensible answer

What you’ll be able to do

• Define the numerator and denominator of a percentage.
• Separate arithmetic from an explanation of what the numbers mean.
• Check an AI-generated calculation against a calculator or spreadsheet.

Start with a question, not a chart

Before asking for analysis, identify the decision you are trying to support. Are you comparing attendance, registrations, or survey responses? A model can calculate the right arithmetic on the wrong population.

Use this fictional workshop dataset:

• Session A: 40 registrations, 32 attendees, 20 survey responses, 18 positive responses.
• Session B: 50 registrations, 35 attendees, 28 survey responses, 21 positive responses.

These are invented examples for practice, not institute operating results.

Work through the arithmetic

Attendance rate means attendees divided by registrations. Session A is 32 ÷ 40 = 80%. Session B is 35 ÷ 50 = 70%.

Positive response rate among survey respondents means positive responses divided by survey responses. Session A is 18 ÷ 20 = 90%. Session B is 21 ÷ 28 = 75%.

Notice that Session B had more positive responses in absolute terms: 21 compared with 18. That does not make its positive response rate higher. Counts and percentages answer different questions.

Separate the result from the story

The data support “Session A had a higher attendance rate.” They do not establish why. Schedule, audience, reminder messages, or many other factors could differ. A suggested explanation is a hypothesis to investigate, not a demonstrated cause.

A tool that can execute calculations may help, but you should still check the inputs and formula. If no calculation tool is available, use a calculator or spreadsheet yourself.

Try a transparent-analysis prompt

Analyze this fictional dataset. Define every metric before calculating it.
Show each numerator, denominator, formula, and result to one decimal place.
Separate observed results from possible explanations. Do not infer causation.
Flag what additional information would help compare the sessions fairly.

A: registrations 40; attendees 32; survey responses 20; positive responses 18.
B: registrations 50; attendees 35; survey responses 28; positive responses 21.

Your practice: build a checked comparison

1. Calculate both attendance rates yourself.
2. Calculate both positive response rates among respondents.
3. Ask the assistant for the same metrics and compare all four results.
4. Ask it to explain whether Session B’s larger positive-response count means higher satisfaction. Check the explanation against the denominators.
5. Write a three-sentence brief: one result, one limitation, and one follow-up question.

Your finished artifact: A calculation sheet and a brief. A strong brief might note the different survey response rates and ask whether the sessions served comparable audiences.

Missing data are not zeros

If a session has no reported survey count, label that field missing. A blank may mean not collected, unavailable, or accidentally omitted. Replacing it with zero without checking changes the analysis. If the denominator is zero, the corresponding rate is undefined rather than automatically 0%.

A common mistake

Choosing the metric after seeing which one makes your preferred option look best. Define the question and metric first, then inspect the results.

Reflection

Name one conclusion the data support and one tempting conclusion they do not support.