Questionnaires and frequency tables — Mathematics, 11–13
Build a questionnaire with closed questions, then organise the answers in a table with absolute and relative frequencies (as percentages).
Closed questions and two kinds of frequency
In a closed question each person picks from a list of answers: “What do you do at break? Football / Cards / Reading / Talking / Other”. The options must cover every case without overlapping, so that each person has exactly one answer. Then you count. The absolute frequency is how many times an answer appears. The relative frequency is that number divided by the total number of answers, a fraction you can write as a percentage. A table needs a title.
Why organise the answers
A pile of 25 slips tells you nothing until you count and record them. A questionnaire with closed questions makes counting fast and avoids answers that cannot be compared. The relative frequency is the useful one when you compare groups of different sizes, because it says what part of each group, not how many. Online forms and spreadsheets can build the table for you, but you still have to check that it makes sense.
A table from 25 answers
25 students answered “What do you do at break?”. Counts: football 10, cards 5, reading 4, talking 5, other 1. Step 1: add the counts, 10 + 5 + 4 + 5 + 1 = 25, the number of slips. If the sum were 26, someone was counted twice or there is a typo. Step 2: relative frequency of football = 10/25. Step 3: 25 × 4 = 100, so 10/25 = 40/100 = 40%. Cards and talking: 5/25 = 20%; reading 4/25 = 16%; other 1/25 = 4%. Check: 40 + 20 + 16 + 20 + 4 = 100%.
10 out of 25 is not 10%
Many people read the count as if it were the percentage: “10 students chose football, so 10%”. But percent means “out of 100”, and here the whole is 25, not 100. Ask: how many would there be out of 100? 25 becomes 100 when multiplied by 4, so 10 becomes 10 × 4 = 40: 40%. The count only equals the percentage when the total is exactly 100. Always start from the whole.
Online forms, sport and school votes
When a school sends an online form, the tool shows you a table with the count and the percentage of each answer. Reports on how students travel to school, sports results and the outcome of a school vote are all built the same way: a total and counts organised in a table. Whenever you see “40%”, ask: 40% of how many?
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