Median locates a middle position
For total frequency N, the grouped median lies in the first class whose cumulative frequency reaches or exceeds N/2.
Learning goals
- Construct and verify a less-than cumulative-frequency column.
- Locate the median class using N/2.
- Calculate grouped median with correct parameters and boundaries.
Concept lesson
Running totals and boundaries
Less-than cumulative frequency is a non-decreasing running total ending at N. Inclusive classes may require continuous boundary correction.
Build cumulative frequency
Start with the first frequency and add each new frequency to the previous total. The final cumulative frequency supplies N and checks the column.
Locate the median class
Compute N/2, scan cumulative frequencies upward, and select the first class with CF at least N/2. Do not seek N/2 in ordinary frequencies and do not choose merely the nearest CF.
Median parameter box
After locating the median class, record l as its lower boundary, f as its ordinary frequency, cf as the cumulative frequency before it, h as width and N as total. Use median=l+[(N/2-cf)/f]h.
Median with inclusive intervals
For classes such as 1-10, 11-20, apply half-gap correction to obtain continuous boundaries, locate the median class by CF and use its corrected lower boundary and width.
Frequency-column separation
Colour ordinary frequency and cumulative frequency differently; calculate CF, mark N/2 on the CF column and identify the first reached class.
N-over-two locator
For several tables, calculate N/2 and identify the first CF at least that value, including cases where N/2 equals a cumulative frequency.
Preceding-CF audit
Draw an arrow from the median class to the previous row's CF, populate the parameter box, calculate and verify the median lies within the median-class boundaries.
Median pipeline across interval formats
Solve exclusive and inclusive tables through the full pipeline—boundaries, CF, N/2, median class, parameters, formula and interval validation—and compare which preparation steps differ.
Median answer protocol
Show cumulative frequencies, N/2 and the selected class; list l, cf, f and h; substitute and confirm the result lies within the class.
Grouped-median mastery
Construct CF, locate median classes in two interval formats, calculate grouped medians and validate both within their class boundaries.