Cumulative frequency
Cumulative frequency is the running total of frequencies up to and including each class, plotted as an ogive to estimate medians and percentiles from grouped data.
See it move
Fifty invoices are grouped as 8 worth €0–€100, 12 worth €100–€200, 20 worth €200–€300 and 10 worth €300–€400. Running these totals gives cumulative frequencies of 8, 20, 40 and 50. The median, at position 25, falls inside the €200–€300 class, and interpolating within it gives an estimated median of €225.
The formula
Variables
- Cumulative frequency through class k
- Cumulative frequency through the previous class
- Frequency of class k
Gives the running total used to build an ogive from a grouped frequency table.
Variables
- Lower boundary of the median class
- Total frequency
- Cumulative frequency before the median class
- Frequency of the median class
- Width of the median class
Estimates the median from grouped data by interpolating within the class where the cumulative frequency first reaches N/2.
Check yourself
A firm groups 50 customer waiting times into classes: 0–5 minutes (6), 5–10 minutes (14), 10–15 minutes (18), 15–20 minutes (12). Using interpolation on the cumulative frequency, what is the estimated median waiting time?