Mean & median traps
Easy stats, careful reading.
← All countdown tipsMean and median answer different questions. The paper will name one and put the other in the options. A single large number pulls the mean up; the median stays in the middle of the ordered list.
Picture it: same five scores, two averages
4, 6, 7, 8, 25
Mean = total ÷ count
50 ÷ 5 = 10 — the 25 pulls it up
Median = middle after ordering
The third value is 7 — ignores the outlier
Remember — name the average
- Mean = total ÷ how many numbers.
- Median = middle after ordering. Even count: mean of the two middle numbers.
- Mode = most frequent. Range = largest − smallest.
Exam trap
They ask for the median of an unsorted list, or the mean after one extra score is added. Order first. Recalculate the new total — do not average the old mean with the new score unless both groups have the same size.
✗ Median of 9, 2, 7 is 2
That is the middle of the written list
✓ Order 2, 7, 9 — median 7
Always sort before you pick the middle
Question patterns you might see
Read the word: mean, median, mode, or range.
1 · Simple — Straight mean
“Mean of 12, 15, 18, 19”
Total
64
→Count
4
→Mean
16
2 · Simple — Unsorted median
Median of 9, 2, 7, 4, 6
- 1Order: 2, 4, 6, 7, 9
- 2Middle: 6
6
3 · Medium — Even count
Median of 3, 5, 8, 12. Already ordered. Middle pair 5 and 8 → (5 + 8) ÷ 2 = 6.5.
4 · Trickier — Find the missing number
“Five scores have a mean of 14. Four of them are 11, 12, 16, 18. What is the fifth?”
- 1Total must be 5 × 14 = 70
- 211 + 12 + 16 + 18 = 57
- 3Fifth = 70 − 57 = 13
13
Coach tip: if they give the mean, immediately write the total (mean × count) in the margin.
Tomorrow (D-4): timing — flag the sticky question and move on.
Next step
Practice locks the idea in. WhatsApp delivers tomorrow’s tip to your phone — same group as mock updates.