Frequency Tables

Learn how to organize data into frequency tables and interpret the results.

Intermediate25 minLesson
Printable worksheet

Definition

A frequency table is a way to organize data by showing how often each value or category occurs.
Key vocabulary:
  • 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)
ValueTallyFrequency
Red4
Blue7
Green3
The total frequency is the sum of all frequencies, which equals the total number of data points.

Try it now

What does "frequency" mean in a frequency table?

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.
1

List each unique value

The colors mentioned are: Red, Blue, Green, Yellow → 4 categories
2

Count Red

Red appears: positions 1, 5, 8, 11, 15, 18 → Red: 6
3

Count Blue

Blue appears: positions 2, 3, 6, 10, 12, 16, 17 → Blue: 7
4

Count Green

Green appears: positions 4, 9, 15, 20 → Green: 4
5

Count Yellow

Yellow appears: positions 7, 13, 19 → Yellow: 3
6

Verify the total

6+7+4+3=206 + 7 + 4 + 3 = 20 → Total matches!

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!

Interactive Visual

Bar Chart

Favorite color (20 students)

Red(6)
Blue(7)
Green(4)
Yellow(3)

Histogram

Homework minutes

10-19(3)
20-29(6)
30-39(4)
40-49(3)

Interactive Sandbox

Expression Calculator

Try these:

History

No calculations yet

Practice Problems

16 problems
Problem 1 of 16
Easy
What does "frequency" mean in a frequency table?

Why It Matters

Frequency tables help us make sense of raw data:
  • 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
Without organizing data, patterns are hidden. Frequency tables reveal what happens most and least often!

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.

1Try It Yourself

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.

2Try It Yourself

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: Choose the right answer

Count each size. Which size sold the most?

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

Frequency is the count (like 5 students). Relative frequency is the proportion or percentage (like 25% of students). Relative frequency = frequency divided by total.
Frequency is the count (like 5 students). Relative frequency is the proportion or percentage (like 25% of students). Relative frequency = frequency divided by total.
Use grouped data when you have many different values (like ages from 1-100) or continuous data. It makes the table easier to read and reveals patterns.
No, tally marks are optional. They're useful while counting data, but the final table often shows just the frequency numbers.

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)
Today's challengeOne problem, three tries

More in This Topic

Reading Bar Graphs

Elementary15 min

Reading Line Graphs

Elementary20 min

Reading Pie Charts

Elementary20 min

Dot Plots

Elementary20 min