Organizing data with counts
A frequency table lists each category (or value) and how many times it appears. The count is called the frequency.
Question: How many pets do students in our class have?
| Number of pets | Tally | Frequency |
|---|---|---|
| 0 | bundle + II | 7 |
| 1 | two bundles | 10 |
| 2 | bundle | 5 |
| 3 | II | 2 |
| 4 or more | I | 1 |
| Total | 25 |
Making a frequency table
- List all the possible categories or values in the first column.
- Go through the data one value at a time, making a tally mark in the right row.
- Count the tallies and write the frequency.
- Add the frequencies. The total frequency should equal the number of data values. If it doesn’t, you’ve missed or double-counted something.
Grouped data and intervals
When data has lots of different values, group them into intervals of equal width.
Test scores: 45, 52, 58, 61, 63, 67, 68, 72, 74, 75, 77, 79, 81, 84, 88, 93
| Score | Frequency |
|---|---|
| 40–49 | 1 |
| 50–59 | 2 |
| 60–69 | 4 |
| 70–79 | 5 |
| 80–89 | 3 |
| 90–99 | 1 |
| Total | 16 |
Make sure intervals don’t overlap and that every value fits in exactly one interval.
Reading a frequency table
From the pets table:
- Most common answer: 1 pet (frequency 10)
- Students with 2 or more pets: 5 + 2 + 1 = 8
- Fraction with no pets: 7/25
From table to graph
A frequency table is the first step to drawing a bar graph or histogram. The categories go along the bottom and the frequencies set the heights of the bars.
Worked examples
Example 1: Data: red, blue, red, green, red, blue. Make a frequency table.
Red 3, blue 2, green 1. Total 6.
Example 2: In the scores table, how many scored 70 or more?
5 + 3 + 1 = 9.
Example 3: A table’s frequencies are 4, 9, 6, 1. How many data values are there?
4 + 9 + 6 + 1 = 20.
Common mistakes
- Overlapping intervals, like 50–60 and 60–70 (where does 60 go?).
- Missing a value when tallying. Cross out each value as you record it.
- Not checking the total frequency.
Try it yourself
Shoe sizes: 4, 5, 5, 6, 4, 5, 7, 6, 5, 4
- Make a frequency table.
- Which size is most common?
- What is the total frequency?
- How many students wear size 6 or larger?
Answers: 1) size 4: 3, size 5: 4, size 6: 2, size 7: 1 2) size 5 3) 10 4) 3
Quick recap
- A frequency table shows how often each value occurs.
- Use tallies while counting and check the total frequency.
- Group lots of values into equal, non-overlapping intervals.