Cumulative relative frequency

Cumulative relative frequency is a running total turned into a proportion. Work through the ordered values or classes and at each one report $\frac{\text{cumulative count}}{n}$, the number of observations at or below that point divided by the total $n$. Two properties fall straight out of that definition, and both are worth checking every time: the column can never decrease, and its final entry must be exactly 1.

Twenty-five students report how many pets they own. Nine own none, eight own one, five own two, two own three, and one owns four. The cumulative counts run 9, 17, 22, 24, 25, so the cumulative relative frequencies are 0.36, 0.68, 0.88, 0.96, and 1.00. That 0.68 says 17 of the 25 students own one pet or fewer.

"The cumulative relative frequency at one pet is 0.68, so 68 percent of the class owns one pet." Exactly one pet is $8/25 = 0.32$. The 0.68 counts everyone at or below one, meaning the nine students with none plus the eight with one. Relative frequency answers how much of the data sits in a category; cumulative relative frequency answers how much sits at or below it. Reading one column as though it were the other is the way this topic usually goes wrong.

The running total only means something when the categories carry an order. Eye color has no notion of at or below, so a cumulative column across blue, brown, and green would report a different answer every time you reordered the rows. Quantitative classes are fine, and so are ordered categories such as never, sometimes, often, always.

The Fall 2026 course framework does not name cumulative relative frequency or the ogive among its representations, so building one is unlikely to be asked. The same arithmetic does appear as percentiles and quartiles in topic 1.7, and reading a cumulative graph handed to you in a stimulus is fair game.