Concept 6 of 7
Mode & Median: Most Common and Middle Value
Today's big idea
Mode = the most frequent value, and median = the middle value once sorted.
Sort before you look, or the middle written number will fool you every time.
How it works
👀 What's going on?
Ask ten children their shoe size and one size will come up again and again. Line the sizes up smallest to largest and one sits dead centre. Those two answers both have names.
💡 Here's the trick
Look at the list above. Sorted, it reads 3, 5, 5, 5, 8, 8, 9, so the middle value is the median. The value that shows up most often is the mode, which here is 5.
🪄 How to do it
- 1.Sort the list smallest to largest, as the list above is sorted.
- 2.Take the middle value for the median, averaging two middles if the count is even.
- 3.Count repeats, and the value with the most is the mode.
✍️ Try it
Find the median and the mode of 4, 7, 4, 9, 6, 4, 11. Then: find the median of 2, 9, 5, 12.
Sorted it is 4, 4, 4, 6, 7, 9, 11, so the median is 6 and the mode is 4. The second list sorts to 2, 5, 9, 12, so the median is (5 + 9) ÷ 2 = 7.
⚠️ Watch out
You might be thinking you can read the median straight off the list as written. Sort it first, every time. In 9, 2, 5 the middle written number is 2, but the median is 5.
🌟 Why this matters
A shoe shop stocks the mode, because that is the size most feet need. House prices are quoted as a median, so one huge mansion cannot drag the figure upwards.
Exam tip: Count the values first, since an even count means you must average the two middle ones.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find the median of: 3, 5, 7, 9, 11.”
- 1
Check it's sorted
3, 5, 7, 9, 11 — already ascending. 🎯
- 2
Count items
5 items (odd count).
- 3
Middle = 3rd item
7
- 4
Answer ✓
Median = 7.
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Mode = the value that appears MOST. Median = the MIDDLE value once the list is sorted.
SHOE SIZES SOLD · STEP 1 OF 3
Tap the value that appears MOST often.
Quick check
✅ VERIFICATION
Find the MODE of: 12, 15, 12, 18, 15, 12, 20.
⚡ Finish the activity above first to answer.
Keep going!
Up next: Range & Multi-Step Data Problems
Sort first → mean · median · mode · range.