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Two Categorical Variables


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?






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?



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