Concept 4 of 7
Frequency & Class-Interval Tables: Counting in Buckets
Today's big idea
Group data into class intervals, where the frequency counts the items per bucket.
Boundary values need one fixed rule, or 20 lands in two buckets at once.
How it works
👀 What's going on?
Thirty quiz scores scattered down a page tell you almost nothing. Sort them into buckets of ten and a shape appears. Suddenly you can see where most of the class landed.
💡 Here's the trick
Look at the table above. Each row is a bucket, and the frequency beside it counts how many values landed inside. Here the buckets are ten wide, and a value on a boundary goes into the higher bucket.
🪄 How to do it
- 1.Set equal buckets, as the table above does.
- 2.Put each value in one bucket only, boundary values going higher.
- 3.Count each bucket, then add the counts for the total.
✍️ Try it
Ages 12, 15, 21, 24, 26, 28, 33, 35 and 41 go into buckets of ten from 10. Which bucket holds the most? Then: how many people are 30 or older?
The buckets hold 2, then 4, then 2, then 1, so the busiest is 20 to 30. Aged 30 or over are 33, 35 and 41, which is 3 people.
⚠️ Watch out
You might be thinking buckets like 10 to 20 and 20 to 30 both take the value 20. Only one can. Pick a rule, such as boundary goes higher, and use it for every row.
🌟 Why this matters
A doctor's growth chart, a cricket score summary and a shop's busiest-hour chart are all frequency counts in disguise. Grouping is what makes a long list readable at all.
Exam tip: Add every frequency and check the total matches the number of people you were given.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Classes 0–10, 10–20, 20–30, 30–40 have frequencies 3, 5, 8, 4. How many items are MORE THAN 20?”
- 1
Find the matching classes
“More than 20” covers 20–30 and 30–40. 🪣
- 2
Add their frequencies
8 + 4
- 3
Compute
12
- 4
Answer ✓
More than 20 = 12.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Frequency = how many times a value appears. Count carefully.
FREQUENCY · ROUND 1 OF 3
How often does 4 appear?
Quick check
✅ VERIFICATION
A frequency table shows 1 pet in 9 homes, 2 pets in 6 homes, 3 pets in 4 homes and 4 pets in 1 home. How many homes have MORE THAN 2 pets?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Mean (Average)
Back-solve: sum = mean × count.