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What do you notice? What do you wonder?
Two-way table
| has cell phone |
does not have cell phone |
total | |
|---|---|---|---|
| 10 to 12 years old | 25 | 35 | 60 |
| 13 to 15 years old | 40 | 10 | 50 |
| 16 to 18 years old | 50 | 10 | 60 |
| total | 115 | 55 | 170 |
Bar graph
Segmented bar graph
When we collect data by counting things in various categories, like red, blue, or yellow, we call the data “categorical data,” and we say that color is a “categorical variable.”
We can use two-way tables to investigate possible connections between two categorical variables.
For example, this two-way table of frequencies shows the results of a study of meditation and state of mind of athletes before a track meet.
| meditated | did not meditate | total | |
|---|---|---|---|
| calm | 45 | 8 | 53 |
| agitated | 23 | 21 | 44 |
| total | 68 | 29 | 97 |
If we are interested in the question of whether there is an association between meditating and being calm, we might present the frequencies in a bar graph, grouping data about those who meditated and those who did not meditate, so we can compare the numbers of calm and agitated athletes in each group.
Double bar graph in blue and red. Horizontal labeled meditated and did not meditate. Vertical labeled 0 to 50, by 10's. Blue represents calm. Red represents agitated.
Notice that the number of athletes who did not meditate is small compared to the number who meditated (29 as compared to 68, as shown in the table).
If we want to know the proportions of calm meditators and calm non-meditators, we can make a two-way table of relative frequencies and present the relative frequencies in a segmented bar graph.
| meditated | did not meditate | |
|---|---|---|
| calm | 66% | 28% |
| agitated | 34% | 72% |
| total | 100% | 100% |
Stacked bar graph in blue and red. Horizontal labeled meditated and did not meditate. Vertical labeled 0 to 100, by 25's. Blue represents calm. Red represents agitated.
The relative frequency of a category tells the proportion at which the category occurs in the data set. It is written as a fraction, decimal, or percentage of the total number.
For example, there were 21 dogs in a park. This table shows the frequency and the relative frequency of each color.
| dog color | frequency | relative frequency |
|---|---|---|
| white | 5 | |
| brown | 7 | |
| black | 3 | |
| multi-color | 6 |
A segmented bar graph shows categories within a data set. Each whole bar represents all the data in one main category. Each bar is separated into parts (segments) that show subcategories.
Stacked bar graph in blue and yellow stripes. Horizontal labeled 10 to 12 years old, 13 to 15 years old and 16 to 18 years old. Vertical labeled 0 to 100, by 25's. Blue section means has cell phone. Yellow stripes means has no cell phone.
This segmented bar graph shows the percentage of people in different age groups that do and do not have a cell phone. For example, among people ages 10 to 12, about 40% have a cell phone and 60% do not.
A two-way table shows data for 2 categorical variables. One variable is shown in rows and the other in columns. Each entry is the frequency or relative frequency of the category shown by the column and row headings.
This two-way table shows the results of a study. The study looked at how meditation affects the way athletes feel.
| meditated | did not meditate | total | |
|---|---|---|---|
| calm | 45 | 8 | 53 |
| agitated | 23 | 21 | 44 |
| total | 68 | 29 | 97 |