# Create and Interpret Two Way Tables

Lesson

## Two Way Tables

Like Venn Diagrams, two way tables are a visual way of representing information.

The two way table below represents how many numbers between 2-20 are even or a multiple of 3.

It's called a two way table because we can read information from it in two directions. If read across each row, we can tell how many numbers are even or not. If we read down each column, we can tell how many numbers are multiples of 3 or not.

Where a particular row and column overlap, these are how many numbers between 2 and 20 satisfy both categories. For example, there are 7 numbers that are even but not a multiple of 3.

Notice that the number in the bottom right cell (19) is how many numbers there are altogether between 2 and 20.

#### Worked Examples

##### QUESTION 1

Dave surveyed all the students in Year $12$12 at his school and summarised the results in the following table:

Play netball Do not play netball Total
Height$\ge$$170$170 cm $46$46 $73$73 $119$119
Height$<$<$170$170 cm $20$20 $39$39 $59$59
Total $66$66 $112$112 $178$178
1. What percentage of Year $12$12 students whose height is less than $170$170 cm play netball?

2. What fraction of the students from Year $12$12 do not play netball?

##### QUESTION 2

In a biology study, the appearance of an animal when carrying a certain gene is recorded. Assume that all animals must cary Gene $A$A or Gene $B$B but not both.

Gene $A$A Gene $B$B
Light fur $36$36 $27$27
Dark fur $28$28 $x$x
1. If, out of all the animals, the proportion carrying Gene A and having light fur is $\frac{4}{19}$419, what is the value of $x$x?

##### QUESTION 3

$36$36 students were asked whether or not they were allergic to nuts and dairy. The two way table is provided below.

Allergic to nuts Not allergic to nuts
Allergic to dairy $10$10 $6$6
Not allergic to dairy $6$6 $14$14
1. How many students are allergic to nuts?

2. How many students are allergic to nuts or dairy, or both?

3. How many students are allergic to at most one of the two things?

### Outcomes

#### S5-1

Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data;– using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings

#### S5-2

Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings