Frequency Tables
Learn how to organize data into frequency tables and interpret the results.
Definition
- Data: Information collected from observations or measurements
- Frequency: The number of times a value appears in a data set
- Tally marks: A quick way to count (|||| = 5)
| Value | Tally | Frequency | ||||||
|---|---|---|---|---|---|---|---|---|
| Red | 4 | |||||||
| Blue | 7 | |||||||
| Green | 3 |
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Worked Examples
A teacher asked 20 students their favorite color. The responses were: Red, Blue, Blue, Green, Red, Blue, Yellow, Red, Green, Blue, Red, Blue, Yellow, Red, Green, Blue, Blue, Red, Yellow, Green. Create a frequency table.
List each unique value
The colors mentioned are: Red, Blue, Green, Yellow → 4 categories
Count Red
Red appears: positions 1, 5, 8, 11, 15, 18 → Red: 6
Count Blue
Blue appears: positions 2, 3, 6, 10, 12, 16, 17 → Blue: 7
Count Green
Green appears: positions 4, 9, 15, 20 → Green: 4
Count Yellow
Yellow appears: positions 7, 13, 19 → Yellow: 3
Verify the total
→ Total matches!
Answer: | Color | Frequency | |-------|----------| | Red | 6 | | Blue | 7 | | Green | 4 | | Yellow | 3 | | Total | 20 |
Common Mistakes
Forgetting to check that frequencies sum to total data points
Why it's wrong: If the sum doesn't match the number of data points, you've miscounted somewhere.
Correct: Always add up all frequencies and verify it equals the total number of data values collected.
Missing a category when counting
Why it's wrong: When scanning through data quickly, it's easy to skip values or count the same one twice.
Correct: Use tally marks and cross off each data point as you count it.
Putting a data value in the wrong interval for grouped data
Why it's wrong: The boundaries can be confusing. Is 20 in '10-20' or '20-30'?
Correct: Decide whether intervals include the left endpoint, right endpoint, or both. Be consistent!
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Practice Problems
16 problemsWhat does "frequency" mean in a frequency table?
Why It Matters
- Sports: Track how many goals each player scored this season
- School: Count how many students got each grade on a test
- Science: Record how many times each outcome occurs in an experiment
- Business: Analyze how many customers visit each day of the week
Real World Applications
Sports Statistics
Coaches use frequency tables to analyze player performance and game outcomes.
Example:
A basketball coach tracks the number of points scored by each player in 10 games to find the most consistent scorer.
A soccer team scored these goals in their last 8 games: 2, 1, 3, 2, 0, 2, 1, 3.
Create a frequency table. What's the most common number of goals?
Step 1: Write the mathematical expression
Count each unique value:
Inventory Management
Stores track product sales using frequency tables to know what to reorder.
Example:
A shoe store counts how many pairs of each size sold this week to stock the most popular sizes.
T-shirt sizes sold today: M, L, M, S, M, L, XL, M, S, L, M, L.
Which size should the store reorder first?
Step 1: Write the mathematical expression
Count each size:
Key Takeaways
- 1A frequency table organizes data by showing how often each value appears
- 2Frequency means the count or number of occurrences of a value
- 3Tally marks (||||) help count data quickly and accurately
- 4The sum of all frequencies must equal the total number of data points
- 5Grouped frequency tables organize data into intervals when there are many different values
Frequently Asked Questions
Glossary
- Frequency
- The number of times a particular value appears in a data set
- Frequency table
- A table that shows each value and how often it occurs
- Tally marks
- A counting method using marks, where |||| crossed = 5
- Grouped data
- Data organized into intervals or ranges rather than individual values
- Interval
- A range of values used to group data (e.g., 10-19, 20-29)