Mean, median, mode — three kinds of 'average': Mean = sum of values ÷ how many. Median = the middle value once the data is ordered. Mode = the value that occurs most often. A question may ask for any one of them.
IB-style question — all three
Find the mean, median and mode of 4, 7, 7, 9, 13.
Step by step
- Mean = sum ÷ n.
- Median = middle of the ordered list (already ordered).
- Mode = most frequent value.
Final answer
Mean = 8, median = 7, mode = 7.
Order the data for the median: Always sort the values before finding the median — the middle of an unordered list is meaningless.
Weight each value by its frequency: When data is in a frequency table, the mean is Σfx ÷ Σf: multiply each value x by its frequency f, add those up, and divide by the total frequency.
IB-style question — mean of a frequency table
The number of siblings of 20 students: 0 → 5 students, 1 → 8, 2 → 4, 3 → 3. Find the mean number of siblings.
Step by step
- Σfx — multiply value × frequency and add.
- Divide by Σf = 20.
Final answer
Mean = 1.25 siblings.
Divide by Σf, not by the number of rows: The denominator is the total frequency (20 here), not the number of different values (4).
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Outliers, and working backwards from the mean: The median is resistant to outliers; the mean is pulled toward extreme values. And if you know the mean, you know the total (sum = mean × n) — use that to find a missing value.
IB-style question — find a missing value
Five numbers have a mean of 12. Four of them are 9, 11, 13 and 15. Find the fifth number.
Step by step
- Total = mean × n.
- Subtract the known four.
Final answer
The fifth number is 12.
When the mean is misleading: If one value is far from the rest (an outlier), quote the median — it better represents a 'typical' value.