Statistics
What is Statistics?
Statistics is the study of collecting, organising, and interpreting data. The four key measures that describe a data set are: mean, median, mode, and range.
Mean (Average)
The mean is calculated by adding all values and dividing by the number of values.
Formula: Mean = Sum of all values Γ· Number of values
Data set: 4, 7, 8, 5, 6 Sum = 4 + 7 + 8 + 5 + 6 = 30 Mean = 30 Γ· 5 = 6
Median (Middle Value)
The median is the middle value when data is arranged in order. It splits the data set in half.
Odd number of values: the middle number is the median.
2, 3, 5, 7, 9 β Median = 5
Even number of values: find the average of the two middle numbers.
3, 5, 7, 9, 11, 13 β Middle values: 7 and 9 β Median = (7+9) Γ· 2 = 8
β οΈ Always sort the data into ascending order first.
Mode (Most Frequent)
The mode is the value that appears most often in the data set.
4, 7, 2, 7, 5, 3, 7 β Mode = 7
A data set can have:
- One mode (unimodal)
- Two modes (bimodal): 2, 2, 5, 5, 8 β modes are 2 and 5
- No mode if all values appear the same number of times
Range (Spread)
The range measures how spread out the data is.
Range = Highest value β Lowest value
Data: 12, 5, 18, 3, 9 Range = 18 β 3 = 15
A small range means data is clustered closely together. A large range means data is spread out widely.
Choosing the Right Measure
| Use | When |
|---|---|
| Mean | Data has no extreme outliers |
| Median | Data has very high or very low outliers that would skew the mean |
| Mode | You want the most common value (e.g. most popular shoe size) |
| Range | You want to understand how spread out the data is |
Example: A footballer's weekly goals: 0, 0, 1, 0, 12 Mean = 13 Γ· 5 = 2.6 β misleading due to the outlier (12) Median = 0 β better represents a typical week