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

What percentage of Year $12$12 students whose height is less than $170$170 cm play netball?

Round your answer to two decimal places.
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`

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?

Enter each line of working as an equation.

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

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

Create and Interpret Two Way Tables

Two Way Tables