Maths: Why Tally Totals Must Match the Sample

A tally chart rests on a simple assumption: each person contributes exactly one mark, so the total number of tallies equals the number of respondents. When that assumption breaks down, the chart stops measuring what it appears to measure. In this survey of 25 students choosing a favourite snack, some students record two choices while others record none, so the tallies no longer map cleanly onto people. The gap between the expected tally total (one per student) and the actual tally total reveals this mismatch directly: expected tallies minus actual tallies exposes how far the data has drifted from a valid count. This matters because a frequency table is only as trustworthy as the responses feeding it. If the total tallies differ from the number of participants, you cannot tell how many students genuinely prefer each snack — the counts are misleading, not merely imprecise. Reliability improves when the survey design itself enforces one response per person, whether through clearer verbal instructions or a structured form listing each option for students to circle once. The mechanism is straightforward: control the response, and the tally total stays equal to the sample size.