Mean, Median & Mode
The three measures of centre answer three different questions. The mean is the balance point — add every value and divide by how many there are; it uses all the data, which is why a single extreme value drags it. The median is the positional middle: sort the list, then take the middle value (or the average of the two middle values if there is an even count); it ignores how far away the extremes are, so it is stable against outliers. The mode is simply the most frequent value, and a set can have one mode, several, or none. The single most useful GRE fact here is the relationship for skewed data: when a distribution has a long tail to the high side, the mean sits above the median; a long low tail pulls the mean below the median. Always sort before you touch the median — the most common error is reading the middle of the unsorted list.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
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Formula Reference Sheet
Measures of centre
| Arithmetic mean | mean = (sum of values) / (number of values) |
|---|---|
| Sum from the mean | sum = mean × n |
| Median (odd n) | the single middle value once sorted |
| Median (even n) | average of the two middle values once sorted |
| Mode | the value(s) that occur most often |
Spread & weighting
| Range | range = greatest value − least value |
|---|---|
| Weighted mean | (Σ weightᵢ × valueᵢ) / (Σ weightᵢ) |
| Missing value | missing = (target mean × n) − (known sum) |
| New mean after adding x | (old sum + x) / (n + 1) |