Definition and position
Big Idea: The median is the middle value when data is ordered. Half the values are below it, half above. Not affected by outliers.
Key difference: Median ≠ Mean when data is skewed. Median is resistant to outliers; mean is not.
Median from raw data
Odd count: use middle: Data: 3, 5, 7, 9, 11 (n=5) Position = (5+1)/2 = 3rd value Median = 7
Even count: average two middle: Data: 3, 5, 7, 9 (n=4) Position = (4+1)/2 = 2.5 → between 2nd and 3rd Median = (5 + 7)/2 = 6
Worked example - Median from raw data
Apply the core method for Median in this section context.
Step by step
- Write the relevant formula or rule first to secure method marks.
- Substitute values from the question carefully and keep units/labels clear.
- Simplify and check whether the result is reasonable in context.
Final answer
Final answer should be clearly stated and interpreted for Median.
Get feedback like a real examiner
Submit your answers and get instant feedback — what you did well, what's missing, and exactly what to write to score full marks.
Try AI Tutor Free7-day free trial • No card required
Median from cumulative frequency
Use CF graph or table: Find position n/2. Read from cumulative frequency graph (ogive) or table at that position.__LINEBREAK__Example: n=100, position=50 Read cumulative frequency table to find value where CF=50.
Worked example - Median from cumulative frequency
Apply the core method for Median in this section context.
Step by step
- Write the relevant formula or rule first to secure method marks.
- Substitute values from the question carefully and keep units/labels clear.
- Simplify and check whether the result is reasonable in context.
Final answer
Final answer should be clearly stated and interpreted for Median.
When to use median
Use median when: ✓ Data contains outliers ✓ Distribution is skewed ✓ You want the most typical value ✓ Working with ranked/ordinal data
Compare mean vs median: If mean >> median → data skewed right (outliers high) If median >> mean → data skewed left (outliers low) If mean ≈ median → data roughly symmetric