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Year 6 Maths Data

Interpret two-way tables

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Theory

A two-way table sorts data by two things at once, such as class and activity. Each cell counts the data that fits its row and its column, and the totals add along rows and down columns. This Year 6 maths page shows how to read a two-way table, use its totals, find missing values and compare groups.

A two-way table has one feature across the top (the columns) and another down the side (the rows).

A cell is where a row and a column meet. In the first diagram, the cell for 6B and Music is \(11\): \(11\) students in 6B chose music.

A row total adds across a row; a column total adds down a column. The grand total (bottom right) counts everyone.

The row totals and the column totals both add to the grand total, because both count every person once.

Two-way table of class and activity A two-way table of the after-school activity of students in 6A and 6B. 6A: sport 13, music 6, art 10, total 29. 6B: sport 8, music 11, art 6, total 25. Totals: sport 21, music 17, art 16, grand total 54. The 6B music cell is shaded. Class Sport Music Art Total 6A 13 6 10 29 6B 8 11 6 25 Total 21 17 16 54
Cell 6B, Music: \(11\). Row total for 6A: \(29\). Grand total: \(54\).
Two-way table of hats at recess A two-way table of girls and boys wearing a hat at recess. Girls: hat 17, no hat 5, total 22. Boys: hat 14, no hat 8, total 22. Totals: hat 31, no hat 13, grand total 44. The Hat column is shaded. Group Hat No hat Total Girls 17 5 22 Boys 14 8 22 Total 31 13 44
Down the Hat column: \(17 + 14 = 31\) students wore a hat.
Two-way table with missing values A two-way table of where lunch came from. Juniors: home 34, canteen missing, total 46. Seniors: home missing, canteen 15, total 41. Totals: home 60, canteen 27, grand total 87. Group Home Canteen Total Juniors 34 ? 46 Seniors ? 15 41 Total 60 27 87
A missing cell is a total take away the other parts of its row or column.

Two-way table rules:

\[ \text{row total} = \text{sum across the row} \]
row total = sum across the row
\[ \text{column total} = \text{sum down the column} \]
column total = sum down the column
\[ \text{row totals added} = \text{grand total} \]
row totals added = grand total
\[ \text{column totals added} = \text{grand total} \]
column totals added = grand total
\[ \text{missing cell} = \text{total} - \text{other cells} \]
missing cell = total − other cells
Row and column. Find the row first, then move across to the column. The answer is the cell where they meet.
The Total row is not a group. The bottom row counts both groups together; do not read it when the question asks about one group.

How to read a two-way table

  1. Find the row for the first feature (for example, the class).
  2. Move across to the column for the second feature (for example, the activity).
  3. Read the cell. For "altogether", use a total.

How to find a missing value

  1. Choose a row or column with only one missing cell.
  2. Subtract the cells you know from that row or column total.
  3. Check that every row and column now adds up.
Example 1 — Read a cell
Use the first table. How many students in 6B chose music?
Solution

Row 6B, column Music: \(11\) students.

Example 2 — Row total
How many students in 6A are in the table?
Solution
\(13 + 6 + 10\)\(=\)\(29\)
13+6+10=29

\(29\) students (the 6A row total).

Example 3 — Column total
How many students chose sport?
Solution
\(13 + 8\)\(=\)\(21\)
13+8=21

\(21\) students.

Example 4 — Grand total two ways
Find the number of students in the table in two ways.
Solution
\(29 + 25\)\(=\)\(54\)
\(21 + 17 + 16\)\(=\)\(54\)
29+25=5421+17+16=54

\(54\) students both ways.

Example 5 — Compare groups
(i) How many more 6A than 6B students chose sport?
(ii) Which activity was chosen by the most students?
Solution
\(13 - 8\)\(=\)\(5\)
13−8=5

(i) \(5\)
(ii) Sport (\(21\) students)

Example 6 — Make the totals
Use the hat table.
(i) How many students wore a hat?
(ii) How many students are in the table?
Solution
\(17 + 14\)\(=\)\(31\)
\(22 + 22\)\(=\)\(44\)
3144

(i) \(31\)
(ii) \(44\)

Example 7 — Missing values
Use the third table.
(i) How many Juniors bought lunch at the canteen?
(ii) How many Seniors brought lunch from home?
Solution
\(46 - 34\)\(=\)\(12\)
\(41 - 15\)\(=\)\(26\)
46−34=1241−15=26

(i) \(12\)
(ii) \(26\). Check: \(34 + 26 = 60\) and \(12 + 15 = 27\).

Example 8 — Grand total two ways
Use the third table. Find the grand total two ways.
Solution
\(46 + 41\)\(=\)\(87\)
\(60 + 27\)\(=\)\(87\)
46+41=87,60+27=87

Down the Total column: \(87\). Along the Total row: \(87\). Both ways give \(87\).

Example 9 — Find the mistake
Zoe says \(21\) students in 6A chose sport. What is wrong?
Solution

\(21\) is in the Total row, so it counts 6A and 6B together. The 6A sport cell is \(13\).

Common pitfalls

Reading the Total row for one group. The Total row adds both groups; read the row for the group you want.
Mixing up rows and columns. Say it aloud: "row 6B, column music" before you read the cell.
Adding a total into a total. Do not add the row total \(29\) to the cells of the same row.
Not checking a missing value. After filling a gap, check that its row and column both add to their totals.

Frequently asked questions

What is a two-way table?

A table that sorts data by two features at once, one across the top and one down the side.

What is the grand total?

The number in the bottom right corner: everyone in the table.

How do I find a missing number?

Subtract the numbers you know from the total of that row or column.

What does a cell show?

The count that fits both its row and its column.

How do I compare two groups?

Read the two cells in the same column and subtract to find the difference.

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