Problem
Complete and interpret a graph
A data table pairs 24 students with the one colour each likes best. Stack that many circles per colour, and the six counts must add to 24. Finish the graph and find every statement among (A)-(E) that is wrong.
Reasoning · Grade 2-2 Tables and Graphs
Your answer
Watch out Purple's 4 wants to join 'fewer than 4', but 4 is not fewer than 4 — which is why (D) is correct.
How to solve
Strategy Make a Systematic List — Counting how many students chose each color is a tally task - go color by color so each of the 24 names is counted once. Once the graph heights are known, each statement (A)-(E) is a claim I test against those numbers (guess-and-check style: read what the statement says, compare to the actual counts, keep it if true or flag it if false).
1STEP 1
Tally each color from the data table
Tallying colour by colour gives 5, 3, 7, 3, 4, 2.
5 + 3 + 7 + 3 + 4 + 2 = 24
Sorting names into color groups one color at a time is the grade-level way to count categorical data without missing or repeating anyone.
1.MD.C.4Make A Systematic List2STEP 2
Draw the graph and check the total
The six add to 24, so the graph is filled correctly.
5+3+7+3+4+2 = 24
Adding the column heights back to 24 confirms every student was placed in exactly one column.
2.OA.B.2Make A Systematic List3STEP 3
Test each statement against the graph
(A)-(D) match the counts; the total is 24 not 23, so only (E) is wrong.
5+3+7+3+4+2 = 24 ≠ 23
Each statement is just a fact to verify against the column heights; only the one that contradicts the numbers (the wrong total) is the incorrect statement.
2.MD.D.10Guess And CheckEach statement is checked against the column heights, and the one that contradicts them is the incorrect statement.
Why?
A statement about the data dies the moment the graph shows a number that disagrees with it, so one clash is enough to rule it out.
🧱One counterexample refutes an always-claimA claim about every case dies the moment you exhibit one case where it fails, and exhibiting is easier than arguing.
Why?
Once every other statement has been confirmed against the graph, the one left over must be the incorrect one.
🧱Rule out the rest and the last one is forcedIf every possibility but one has been ruled out, the survivor must be the answer — no further checking is needed.
Answer
red 5, blue 3, yellow 7, green 3, purple 4, pink 2, total 24 / only (E) is wrong
The six color counts add to exactly 24, the stated class size, so the graph is consistent. Statements (A)-(D) each match the actual heights, and (E) fails only because it says 23 instead of 24 - so flagging exactly (E) is sensible.
Takeaway
Count each color into its own stack of circles, then add them up - the heights tell the truth, and statement (E)'s total of 23 simply doesn't match the real 24.
- Tally each color from the data table
- Draw the graph and check the total
- Test each statement against the graph