Concept 7 of 7
Range & Multi-Step Data Problems
Today's big idea
Range = largest − smallest, which measures how spread out the data is.
Range shows how far apart the two ends sit, not where the numbers actually are.
How it works
👀 What's going on?
Two batsmen both average 40 runs a match. One scores near 40 every single time, the other swings from 5 to 90. An average alone will never tell you that.
💡 Here's the trick
Look at the number line above. The dots run from 3 up to 11, so the range is 11 − 3 = 8. A small range means the values huddle together, and a large range means they spread wide.
🪄 How to do it
- 1.Sort the values, the way the number line above is sorted.
- 2.Take the smallest from the largest to get the range.
- 3.Read off the median and mode, and work out the mean if asked.
✍️ Try it
Daily rainfall in mm was 8, 22, 14, 6, 20 and 14. Find the range. Then: find the mean, and give the range minus the mean.
The largest is 22 and the smallest is 6, so the range is 16. The six values total 84, so the mean is 14, and 16 − 14 = 2.
⚠️ Watch out
You might be thinking the range tells you where the numbers are. It only tells you how far apart the two ends sit. The lists 1, 9 and 101, 109 both have a range of 8.
🌟 Why this matters
A weather report gives the day's high and low, and the gap between them is the range you will feel. Factories check the range of a machine's output to spot a fault early.
Exam tip: Sort the list once, then read the range, median and mode straight off it.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find the RANGE of: 20, 8, 15, 11, 26.”
- 1
Spot max & min
Max = 26. Min = 8. 📏
- 2
Range = max − min
26 − 8
- 3
Compute
18
- 4
Answer ✓
Range = 18.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Range = biggest value − smallest value. It measures how spread out the data is.
TEST SCORES · ROUND 1 OF 3
Tap the BIGGEST value.
Quick check
✅ VERIFICATION
The tallest boy is 148 cm and the range of the heights is 26 cm. How tall is the shortest boy?
⚡ Finish the activity above first to answer.
Keep going!