IRTVD - Two-Way Frequency Tables (Lesson)
Two - Way Frequency Tables
In the previous module, we discussed numerical data. Numerical data is data you can count or measure. For instance, the heights of players on your basketball team can be classified as numerical data. You will continue to learn about numerical data, but we will also discuss categorical data. Categorical data is data that represents characteristics such as the type of a pet a person has, or their favorite type of food.
The frequency of a data value is the number of times it occurs and we often display this type of data in a frequency table.
The frequency table below shows the results of a survey that Jana took at her school. She asked 40 randomly selected students whether they preferred pizza, burgers or some other type of food.
|
|
Preferred Food |
|||
|---|---|---|---|---|
|
|
Pizza |
Burgers |
Other |
Total |
|
Frequency |
18 |
12 |
10 |
40 |
While a frequency table is helpful for organizing data, a relative frequency table allows us to see the data as a decimal and more importantly a percent. We can convert Jana's original table to a relative frequency table by dividing the number of responses in favor of each food by the total number of responses.
|
|
Preferred Food |
|||
|---|---|---|---|---|
|
|
Pizza |
Burgers |
Other |
Total |
|
Relative Frequency |
18/40 = 0.45 |
12/40 = 0.3 |
10/40 = 0.25 |
1 |
Now let us convert the decimals to percent's.
|
|
Preferred Food |
|||
|---|---|---|---|---|
|
|
Pizza |
Burgers |
Other |
Total |
|
Relative Frequency |
45% |
30% |
25% |
100% |
Jana also recorded the gender of each student who responded to her survey and has given it in a two-way frequency table. Each entry is the frequency of students who prefer a certain food and are of a certain gender. For instance, 7 girls prefer burgers as food.
|
|
|
Preferred Food |
|||
|---|---|---|---|---|---|
|
|
|
Pizza |
Burgers |
Other |
Total |
|
Gender |
Girl |
8 |
7 |
1 |
|
|
Boy |
10 |
5 |
9 |
|
|
|
Total |
|
|
|
|
|
- How many total girls took part in the survey?
- How many total boys took part in the survey?
- Why should your answers from #1 and #2 add to 40?
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
Notice that the totals for each column are the same as the first table you were given. And if you combine the values in that row you will also get 40.
|
|
|
Preferred Food |
|||
|---|---|---|---|---|---|
|
|
|
Pizza |
Burgers |
Other |
Total |
|
Gender |
Girl |
8 |
7 |
1 |
16 |
|
Boy |
10 |
5 |
9 |
24 |
|
|
Total |
18 |
12 |
10 |
40 |
|
You can obtain the following relative frequencies from a two-way frequency table:
- A joint relative frequency is found by dividing a frequency (not from the total row) by the grand total.
- A marginal relative frequency is found by dividing a row or column total by the grand total.
Watch this video to convert Jana's table to a two-way relative frequency table.
Watch this video to try another problem.
John took a survey of 50 random students at his school to determine his classmate's preferences of sports. Given the following information, fill out the two-way frequency table:
- 28 boys were surveyed
- 6 girls preferred football and 8 preferred basketball
- 12 boys preferred football and 2 preferred softball
|
|
|
Preferred Sport |
|||
|---|---|---|---|---|---|
|
|
|
Basketball |
Football |
Softball |
Total |
|
Gender |
Girl |
Solution |
Solution |
Solution |
Solution |
|
Boy |
Solution |
Solution |
Solution |
Solution |
|
|
Total |
Solution |
Solution |
Solution |
Solution |
|
Create a two-way relative frequency table using decimals:
|
|
|
Preferred Sport |
|||
|---|---|---|---|---|---|
|
|
|
Basketball |
Football |
Softball |
Total |
|
Gender |
Girl |
Solution |
Solution |
Solution |
Solution |
|
Boy |
Solution |
Solution |
Solution |
Solution |
|
|
Total |
Solution |
Solution |
Solution |
Solution |
|
Find the joint relative frequency that a student is a girl and prefers football.
Find the joint relative frequency that a student prefers softball and is a boy.
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
Conditional Relative Frequencies
A conditional relative frequency allows you to find the frequency of an event happening given a certain piece of information. Watch this video to try a few:
Anthony surveyed 60 of his classmates about their participation in school activities as well as whether they have a part-time job. The results are shown in the two-way frequency table below.
|
|
|
Activity |
||||
|---|---|---|---|---|---|---|
|
|
|
Clubs Only |
Sports Only |
Both |
Neither |
Total |
|
Job |
Yes |
12 |
13 |
16 |
4 |
Solution |
|
No |
3 |
5 |
5 |
2 |
Solution |
|
|
Total |
Solution |
Solution |
Solution |
Solution |
Solution |
|
- Find the totals for each row and column.
- Find the conditional relative frequency that a student surveyed plays sports only given that the student does have a job.
- Find the conditional relative frequency that a student surveyed does not have a job given that the student participates in clubs only.
- Find the conditional relative frequency that a student surveyed is involved in both clubs and sports given that the student does have a job.
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
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