1. Two-Way Tables & Stepped Tables
Mathematics
Two-Way Tables & Stepped Tables

2. Lesson Objectives The aim of this powerpoint is to help you…
to learn how to complete, read and interpret a two-way table
to learn how to use a stepped table

3. Two-Way Tables
This table is used to summarise data using two different criteria.
One criterion will apply to the rows of the table and the other criterion will apply to the columns.
The total number of objects included in the data will EITHER equate to the total of the rows OR the total of the columns (they should be equal!).

4. Two-Way Tables
Read the question carefully and find the correct row(s) and/or column(s) referred to, in order to work out the answer.
If there are missing values in the table, use the information you have been given in the question to work out the missing values.
Remember, rows should have a total at the end – subtract individual row values from the row total to find missing row values.
Remember columns should have a total at the bottom – subtract individual column values from the column total to find missing column values.

5. Using Two-Way Tables - Example
The two way table below shows the genders and writing hands of students in a small primary school.
You will need to use this table to answer the questions that follow.
GIRLS
BOYS
RIGHT-Handed 52 83
LEFT-Handed 6 8

6. Using Two-Way Tables - Example
Q1. How many girls write with their left hand?
HINT: Look down the ‘girls’ column and across the ‘left’ row.
What value is in the overlapping section?
ANS. 6
GIRLS
BOYS
RIGHT-Handed 52 83
LEFT-Handed 6 8

7. Using Two-Way Tables - Example
Q2. How many girls are there altogether?
HINT: Look down the ‘girls’ column and total these values.
ANS = 58
GIRLS
BOYS
RIGHT-Handed 52 83
LEFT-Handed 6 8

8. Using Two-Way Tables - Example
Q3. How many students are right-handed?
HINT: Look across the ‘right-handed’ row and total these values.
ANS = 135
GIRLS
BOYS
RIGHT-Handed 52 83
LEFT-Handed 6 8

9. Using Two-Way Tables - Example
Q4. How many students are there altogether?
HINT: Add ALL the values together.
ANS = 149
GIRLS
BOYS
RIGHT-Handed 52 83
LEFT-Handed 6 8

10. Completing Two-Way Tables - Example
This table shows the genders and dominant hands of another group of students.
There are 50 students in the class and 7 are left-handed. Fill-in the missing table values.
Let’s do this step-by-step…
GIRLS
BOYS
LEFT-Handed 2
RIGHT-Handed 17

11. Completing Two-Way Tables - Example
First let’s put in the total rows and columns…
Now let’s put in the fact we have been told that are 50 students in the class…
Finally we are also told 7 students are left-handed…
GIRLS
BOYS
LEFT-Handed 2
RIGHT-Handed 17
GIRLS
BOYS
TOTAL
LEFT-Handed 2
RIGHT-handed 17 7 50

12. Completing Two-Way Tables - Example
Left-handed row: 2 + ? = 7 …. Boys = 7 – 2 = 5
Total column: 7 + ? = 50 … Right = 50 – 7 = 43
Boys column: = 22
GIRLS
BOYS
TOTAL
LEFT-Handed 2 7
RIGHT-handed 17 50 5 43 22

13. Completing Two-Way Tables - Example
Right-handed row: ? + 17 = 43 …. Girls = 43 – 17 = 26
Girls column: = 28
CHECK using Total row: = 50 (Yes)
GIRLS
BOYS
TOTAL
LEFT-Handed 2 5 7
RIGHT-handed 17 43 22 50 26 28

14. Stepped Tables
This type of table again has two directions (rows and columns) but usually applies to one criterion.
These tables are usually used to indicate distances between places.
Place names appear in both a row and a column – there are two ways of displaying them too!
Distances between places are where those places’ rows and/or columns overlap.

15. Stepped Tables - Example
Both stepped tables below show the distances between 5 towns (A to E). They are merely labelled slightly differently.
The one on the right is the more typical style of labelling. A B C D E 7 12 23 35 5 19 40 13 58 62 7 12 23 35 5 19 40 13 58 62 B C D E
A B C D

16. Stepped Tables - Example
How far is it from B to C?
HINT: Which row/column do B and C overlap in?
ANS. 5 A B C D E 7 12 23 35 5 19 40 13 58 62 7 12 23 35 5 19 40 13 58 62 B C D E
A B C D

17. What next?
Print out and read through the notes called Data8a & Data8b.
Work through the MyMaths lesson and then its online homework called Two Way Tables which can be found at:
Lesson:
Online HW:
Answer the tasks that appear in the Data8a & Data8b notes.
Learn about another type of stepped representation by working through the MyMaths lesson and then its online homework called Step Graphs found at:
Lesson:
Online HW:
Now move on to the Data-9 powerpoint