Knowledge Organiser: Averages (Mean, Median, Mode)
Key Terms
- Mean: Sum of all values divided by the number of values
- Median: The middle value when data is arranged in order
- Mode: The value that appears most often
- Outlier: An extreme value that skews the mean
- Bimodal: Data with two modes (equally frequent values)
- Average: A single representative value summarising a dataset
Must-Know Facts
- Mean uses every value in the dataset; outliers distort it
- Median is unaffected by extreme outliers: use for skewed data
- Mode is the only average that works for categorical (non-numerical) data
- For an even number of values, median = mean of the two middle values
- Data can have no mode, one mode, or multiple modes
- To find a missing value: missing = (mean × n) − sum of known values
- The mean should always lie between the minimum and maximum values
Key Formulas
- Mean = (sum of all values) ÷ (number of values)
- Median position = (n + 1) ÷ 2 (for n values)
- Missing value = (mean × n) − sum of known values
Common Mistakes
- Median with an even number of values: Median is the average of the two middle values: add them and divide by 2
- Mode vs most common: Mode is the value that appears most often: there can be more than one mode or none
- Mean affected by outliers: A single very high/low value pulls the mean but not the median: choose the appropriate average
- Median position: For n values, median is at position (n+1) ÷ 2: don't just pick the middle value without finding its position