Concept 8 of 9
Frequency Tables: Grouping into Buckets
Today's big idea
Equal-width bands turn a list too long to read into a few rows you can compare.
Bands must be equal width, and a value on a boundary needs one clear rule.
How it works
👀 What's going on?
Thirty test scores in a long list tell you almost nothing. The same thirty sorted into four bands tell you at a glance where most of the class landed.
💡 Here's the trick
A frequency table counts how many items fall at each value, or into each band of values. When there are too many different values to list, you group them into bands of equal width. A value sitting exactly on a boundary goes into the higher band.
🪄 How to do it
- 1.Read the bands down the side of the picture above and check they are all the same width.
- 2.Put each value into its band, sending a value on a boundary to the higher one.
- 3.Count each band to get its frequency.
✍️ Try it
The bands are 0 to 10, 10 to 20, 20 to 30 and 30 to 40. The scores are 12, 25, 8, 31, 19, 22, 7, 28, 15 and 33. How many land in the first band, and how many in the third?
The first band takes 8 and 7, so its frequency is 2. The third band takes 25, 22 and 28, so its frequency is 3.
⚠️ Watch out
A value on a boundary belongs to the higher band. A score of exactly 20 goes into 20 to 30 and not into 10 to 20. Forgetting that moves one item and changes two frequencies at once.
🌟 Why this matters
Bands are how anyone makes sense of a big pile of numbers. Ages at a family party, heights across a class, how long each child took to finish a race.
Exam tip: Tick each value off the list as you place it, because the frequencies have to add back up to however many values you started with.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Class table: 0-10 → 5, 10-20 → 6, 20-30 → 9, 30-40 → 2. How many MORE THAN 20?”
- 1
Find matching classes
“More than 20” covers 20-30 and 30-40. 🪣
- 2
Add frequencies
9 + 2
- 3
Compute
11
- 4
Answer ✓
More than 20 = 11
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 table has bands 0-10, 10-20, 20-30 and 30-40. Which band does a score of exactly 20 go into?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Mean (Average)
Back-solve: sum = mean × count.