Graphs, Tables & Averages

OC graphs use grown-up scales: gridlines counting by 10, small lines by 2. First job on ANY graph — before touching the question — decode the scale: 'one gridline = 10, one small line = 2'. A typical reading graph has bars at 15, 35, 42, 21 and 12: misjudge the scale and every later step collapses. Scale first, bars second, question third.

The OC's favourite data format: someone makes claims about a graph, and you verdict each one. Example — a reading graph, three claims: 'more than 80 read 1 or 2 books' (35 + 42 = 77 — false), 'exactly three times as many read 2 books as 0 books' (42 vs 15 — 3 × 15 is 45, so false; 'exactly' means exactly!), '20 more read 1 book than 0 books' (35 − 15 = 20 — true). Only claim 3 stands. The discipline: arithmetic for every claim, and merciless precision on words like 'exactly' and 'more than'.

OC style: two bar graphs — Team A scored 31 over the season, Team B has 28 with one game to go. Smallest last-game score so Team B BEATS Team A? 'Beats' means strictly more: 31 doesn't beat 31, so the target is 32 — needing 32 − 28 = 4. The trap option 3 (which only ties) is right there in the choices. Two-graph questions are: total both, compare, and read the inequality word ('beats', 'at least', 'no more than') with lawyer's eyes.

The average (mean) is the fair-share level: if the towers 5, 8, 2, 5 shared their blocks equally, each would hold 5 — because the total (20) divided by the count (4) is 5. That's the whole formula: mean = total ÷ how many. And it runs backwards beautifully: 'four tests average 6' means the TOTAL was 24 — often the fact a puzzle really needs.

The OC's favourite average question runs backwards: four tests average 8; the first three scored 7, 9, 6 — find the fourth. Convert the average to a TOTAL: 4 × 8 = 32 needed. Sum the knowns: 22. The missing score: 32 − 22 = 10. Averages are handled through totals — never add or subtract the average itself. This 'average × count = total' bridge, plus the claim-verification and scale-reading habits, completes your data toolkit. Quiz and exercises!