# 1.3.5.5: Cumulative Frequency and Relative Frequency

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The cumulative frequency of a class interval is the count of all data values less than the right endpoint. The cumulative relative frequency of a class interval is the cumulative frequency divided by the sample size.

Definition: Cumulative Relative Frequency

n = sample size ‐ The number of observations in your sample size.

Cumulative Frequency ‐ the number of times a particular value is observed in a class interval or in any lower class interval.

Cumulative Relative Frequency ‐  The proportion or percentage of times a particular value is observed in a class interval or in any lower class interval.

Cumulative Relative Frequency = Cumulative Frequency / n

Example: Students browsing the web

Let's again return to the data that represents how much time 30 students spent on a web browser in a 24 hour period. Data is rounded to the nearest minute. Earlier we had made a frequency distribution and so we will now add columns for cumulative frequency and cumulative relative frequency.

Note that the last class interval will always have a cumulative relative frequency of 100% of the data.

Some possible ways to interpret cumulative relative frequency: 83.3% of the students are on the internet less that 115 minutes.

The middle value (median) of the data occurs in the interval 91 to 103 minutes since 53.3% of the students are on the internet less than 103 minutes.

Example: Comparing weights of apples and oranges

The tally feature of Minitab can also be used to find cumulative relative frequencies (called cumulative counts and percentages here):

Cumulative relative frequency can also be used to find percentiles of quantitative data. A percentile is the value of the data below which a given percentage of the data fall.

In our example 280 grams would represent the 69th percentile for apples since 69% of apples have weights lower than 280 grams. The 68th percentile for oranges would be 310 grams since 68% of oranges weigh less than 310 grams.

1.3.5.5: Cumulative Frequency and Relative Frequency is shared under a CC BY-SA license and was authored, remixed, and/or curated by LibreTexts.