A chart pairs each of 28 students with the one fruit they like best - apple, yellow apple, persimmon, grapes, tangerine, banana or cherry. Counting per fruit fills a table whose total must come to 28. Five claims are offered: (A) which fruit Eunju likes, (B) how many students like grapes, (C) which fruit the most students like, (D) who likes the same fruit as Jihyeon, (E) whether more boys than girls like bananas. Fill the table, then pick the claims the table alone settles.
Your answer
Watch outThe picture knows it, so the table seems to as well — but a count table keeps only 'how many' and drops 'who' and 'gender'.
How to solve
StrategyMake a Systematic List — Counting categories from raw data is exactly a 'make a systematic list / tally' task: go fruit by fruit so nobody is missed or double-counted. For part (2) I change the representation in my head from the raw name-by-fruit data to the summary frequency table and ask what information survives that re-organizing - the table keeps the per-fruit counts but loses individual names and gender, which decides each statement.
1STEP 1
Tally each fruit one category at a time
Sweeping one fruit at a time gives 3, 5, 2, 5, 2, 4, 7.
3 + 5 + 2 + 5 + 2 + 4 + 7 = 28
Going category by category - tallying one fruit completely before the next - is the grade-level way to sort data into categories without missing or repeating anyone.
1.MD.C.4Make A Systematic List
2STEP 2
Fill the table and check the Total
The seven counts add to 28, so nobody was missed.
3+5+2+5+2+4+7 = 28
The Total is just the seven category counts added up; matching it to the known 28 students is a quick self-check on the tally.
2.OA.B.2Make A Systematic List
The seven category counts must add back to 28, which is why the total is a real check on the tally.
Why?
Each student picked exactly one fruit, so every student is counted in one category and never in two.
🧱Disjoint cases addSplit the possibilities so no case overlaps another and none is left out, and the case counts simply add.
Why?
The seven categories between them cover the whole class, so their counts put together are the size of the class.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
3STEP 3
Decide what the frequency table alone can tell you
Only counts survive, so just (B) and (C) are knowable.
A summary graph/table answers 'how many' and 'which is most' questions but cannot answer 'who' or 'boys vs girls' once the individual rows are collapsed into counts.
2.MD.D.10Organize Information In More Ways
Answer
apple 3, yellow-apple 5, persimmon 2, grapes 5, tangerine 2, banana 4, cherry 7, total 28 / knowable (B), (C)
The seven counts add to exactly 28, the stated class size, so the table is consistent. For part (2), (B) and (C) are pure 'how many / which is most' questions that a count table is built to answer, while (A), (D), (E) ask about a specific student or about gender - information the table does not contain - so rejecting those three is sensible.
Takeaway
Count each fruit carefully so everything adds to 28 - then remember a count table tells you 'how many' and 'which is most,' but never 'who' or 'boy or girl.'
Tally each fruit one category at a time
Fill the table and check the Total
Decide what the frequency table alone can tell you