Two categories across, two down, and the margins that hold them together. These free printable worksheets fill the gaps and find the relative frequencies.
A two-way table sorts the same group of people two ways at once — which grade they are in AND whether they have a pet — and the whole of reading one is knowing that every number belongs to a row and to a column at the same time. The margins are not decoration: they are the totals those rows and columns add up to, and they are what makes a gap findable.
Why this sheet works
So the first setting blanks one number and prints all the totals. It is a subtraction, and the arithmetic is not the point — knowing which row and which column the gap sits in is. There are two ways to it, along the row and down the column, and they have to agree; a student who checks one against the other has understood the structure rather than followed an instruction.
How this one works
One question from this sheet, worked through a step at a time.
Every number in a two-way table belongs to a row AND to a column. The gap is in the Afternoon row and the Swim column, so either one of them can find it — and if both give the same answer, it is right.
Along the row first. The Afternoon row adds up to 50, and the other number in it is 15. So the gap is 50 − 15 = 35.
Down the column as a check. The Swim column adds up to 55, and the other number in it is 20: 55 − 20 = 35. The same 35, which is what says the table hangs together.
So the missing number is 35 — the Afternoon row totals 50, and 50 − 15 = 35.
Read each table. Fill the gap, or answer the question under it.
1
Swim
Hike
Total
Morning
20
24
44
Afternoon
15
50
Total
55
39
94
2
Finished
Gave up
Total
Indoors
8
2
10
Outdoors
24
4
28
Total
32
6
38
Of the 10 indoor teams, what percent finished?
%
3
Cash
Card
Total
Weekday
14
6
20
Weekend
5
10
Total
19
11
30
4
Swim
Hike
Total
Morning
6
10
16
Afternoon
3
22
25
Total
9
32
41
Of the 25 afternoon campers, what percent chose to swim?
%
Two-way tables · Gaps and percentsAnswer key
1. Afternoon and Swim = 352. Of the 10 indoor teams, what percent finished? 80%3. Weekend and Card = 54. Of the 25 afternoon campers, what percent chose to swim? 12%
