NZ Level 3
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Two Categorical Variables
Lesson

We've already looked at how we can use a table to display data we collect. Normally this is based on one group who may answer in a certain number of ways. For example, you could ask everyone in your class to choose their favourite type of juice and display your results in a graph or table, such as the one below.

Type of Juice Number of People
Apple $12$12
Pineapple $4$4
Orange $8$8
Tropical $5$5

 

But what would we do if we wanted to know whether there were differences in juice preferences between boys and girls? Well, we would need to create a two-way table. Let's learn how to do this.

Let's recap the video:

To create a two-way table, we list the different groups along one side of the table and the different categories on the other, like so:

Type of Juice Boys Girls
Apple $5$5 $7$7
Pineapple $3$3 $1$1
Orange $6$6 $2$2
Tropical $2$2 $3$3

Notice how the two groups, boy and girls, are the headings for the columns and each variable (i.e. each type of juice) is a separate heading for each row? Now we get even more information! For example, I can say apple juice was preferred by most girls ($7$7 girls picked it), while most boys preferred orange juice ($6$6 picked it). Or I could say $2$2 more boys preferred pineapple juice than girls (because $3-1=2$31=2).

We can also display our results in a graph, with the two groups side-by-side, like in the column graph below:

 

Worked Examples

Question 1

Mr. Westwood asked the students in his class to pick whether they prefer swimming or cycling. He displayed the results in a two-way table.

  Boys Girls
Swimming $11$11 $14$14
Cycling $7$7 $11$11
  1. How many boys picked swimming?

  2. How many girls picked cycling?

  3. Did more boys prefer swimming or cycling?

    Swimming

    A

    Cycling

    B

    Swimming

    A

    Cycling

    B

 

Question 2

Maximilian asked his staff which mode of transport they took to work. He displayed his results in a two-way table.

  Males Females
Train $12$12 $17$17
Bus $19$19 $9$9
  1. How many males caught the bus?

  2. How many more females caught the train than the females that caught the bus?

  3. How many males did Maximilian survey in total?

 

 

Outcomes

S3-1

Conduct investigations using the statistical enquiry cycle: – gathering, sorting, and displaying multivariate category and wholenumber data and simple time-series data to answer questions;– identifying patterns and trends in context, within and between data sets; – communicating findings, using data displays

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