Interpreting results
Two-way tables
A frequency table shows one thing. A two-way table shows two at once — how a hockey team did, split by home and away, all in one grid.
From one set of data to two
A FREQUENCY TABLE is good for showing ONE piece of information — how many people sent 0–9 texts, 10–19 texts, and so on. But often you want two things at once. A TWO-WAY TABLE records two sets of DISCRETE DATA by putting one in the rows and the other in the columns.
Reading a cell
Each cell sits where a row and a column meet, and it counts the things that are in BOTH. For a hockey team's season: Win Draw Lose Total Home 7 3 2 12 Away 3 4 5 12 Total 10 7 7 24 Home games lost? Go along the 'Home' row to the 'Lose' column: 2.
The totals row and column
The last row and last column hold the TOTALS. • Games drawn altogether: the 'Total' row, 'Draw' column → 7. • Games played altogether: bottom-right corner → 24. That bottom-right number is the grand total. It should equal the row totals added up AND the column totals added up — a built-in check.
Filling in a missing value
Because every row and column adds to its total, you can work out any missing cell. If the Away row shows 3 wins, 4 draws and a total of 12, then the losses must be 12 − 3 − 4 = 5 Subtract what you know from the total.
Worked examples
How many home games were lost?
- Find the 'Home games' row.
- Follow it to the 'Lose' column.
Answer: 2
How many away games were won?
- Find the 'Away games' row.
- Follow it to the 'Win' column.
Answer: 3
How many games were drawn altogether?
- Go to the 'Total' row.
- Read the 'Draw' column.
Answer: 7
How many games were played in the season?
- The grand total is the bottom-right cell.
Answer: 24
Filling a gap: away games with 3 wins, 4 draws, 12 total
- The row must add to 12.
- 12 − 3 − 4 = 5.
Answer: 5 losses
Checking a two-way table
- Add the row totals.
- Add the column totals.
- Both should equal the grand total.
Answer: Both give 24, so the table is consistent
Where you see this in real life
- Exam results are often published as a two-way table of grade against subject, so you can compare in either direction.
- A shop's sales table splits takings by branch and by month, which is how they spot a branch having a bad quarter.
Key words
- Two-way table
- a table recording two sets of data, in rows and columns
- Frequency table
- a table showing how often each value occurs
- Discrete data
- data you count, in separate whole values
- Total
- the sum of a row or column
- Cell
- one box in a table, where a row meets a column