The Misleading Attendance Graph
A class of 40 students had attendance of 92% in Term 1, 88% in Term 2, and 85% in Term 3. A student preparing a report plots the three values on a bar chart whose vertical axis starts at 80% instead of 0%. On this chart, the Term 1 bar looks roughly four times taller than the Term 3 bar. The student concludes attendance "collapsed" and proposes a strict new policy. The class teacher points out that 85% still means 34 of 40 students present on a typical day. The report will be shown to the school board, which has limited time and tends to react to visuals.
1. Explain why the chart exaggerates the decline, using the numbers.
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With the axis starting at 80%, bar heights represent the value minus 80: Term 1 = 92 − 80 = 12 units, Term 3 = 85 − 80 = 5 units. The ratio of drawn heights is 12 ÷ 5 = 2.4, and depending on exact scaling can look close to 4× if the baseline is drawn loosely.
The true change is 92% → 85%, a drop of 7 percentage points, or about 7.6% relative decline. On a zero-based axis the bars would be 92 and 85 - nearly the same height.
So the visual message (collapse) contradicts the data (a modest decline). Truncating the axis is the cause: it removes the shared baseline that makes bar lengths proportional to values. The chart is technically not false but is seriously misleading.
2. The teacher says 85% is 34 of 40 students. Verify and explain what this adds to the debate.
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85% of 40 = 0.85 × 40 = 34 students present, 6 absent. Term 1: 92% of 40 = 36.8, so about 37 present, 3 absent. Term 2: 88% of 40 = 35.2, about 35 present, 5 absent.
So the change from Term 1 to Term 3 is roughly 3 extra absences per day (3 → 6), not a collapse. The absolute framing is more honest about scale.
Caveat: percentages of 40 move in steps of 2.5% (1 student = 2.5%), so 92% and 88% are not exactly achievable counts - they are rounded. A careful report should state counts (37, 35, 34) and note rounding, rather than implying precision the data lacks. This strengthens the teacher's point without overclaiming.
3. The student wants to keep the chart because it "gets attention." Advise on what to present to the board.
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Attention gained by distortion backfires when the board discovers the axis trick - credibility is lost and the policy proposal is discredited along with the chart.
Recommended presentation: a zero-based bar or line chart showing 92, 88, 85, plus a small table of student counts (37, 35, 34) and absences (3, 5, 6). If the decline matters, show the counts of absences, which makes the real change visible without distortion.
If a truncated axis is ever used, label it clearly and explain why (small changes matter). But for a board with limited time, clarity beats drama.
Judgement: the honest chart still supports concern (absences doubled from 3 to 6) without exaggeration. Argue the policy on the absence counts and their causes, not on a visual illusion.