cumfreq() — Cumulative frequency

A rising line of the running total up to each value.

plot(edges, cumsum(counts))

Key idea

• A cumulative frequency graph plots the running total of counts up to each value. (e.g. 5, then 5+8=13, then 13+10=23)
• The line only rises or stays level, ending at the total number of values. (e.g. ends at 50)
• Read across at half the total, then down, to estimate the median (the middle value). (e.g. half of 50 = 25)
• Reading at a quarter and three quarters of the total gives Q1 and Q3 (lower and upper quartiles). (e.g. Q1 at 12.5, Q3 at 37.5)
• A steep section shows where many values are bunched together.

Definition

$$\text{median}=L+\frac{\frac{n}{2}-F}{f}\times h$$

$L$

lower edge of the median class

$n$

the total count

$F$

cumulative count before that class

$f$

frequency of that class

$h$

the class width

$$\text{median}=20+\frac{19-13}{14}\times 10=20+4.29\approx 24.3$$

In plain words

Keep a running tally as you move right; the line climbs step by step until it reaches everyone.

Where you'd use it

• From test scores grouped as 50–60: 3, 60–70: 8, … you can read off how many students scored under 70 — just look up the line at x = 70.
• Plot cumulative sales by price band, then read across from half the total to estimate the median price.
• Group 200 waiting times into 10-minute bands; the curve shows what fraction of customers were served within any chosen time.

Frequently asked questions

Can cumulative frequency go down?

No — it only ever increases. A drop means a data-entry error.