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1.3.5.5: Cumulative Frequency and Relative Frequency

  • Page ID
    28665
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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.

    clipboard_ecda7352eeba89239ec3359f0858814c6.png

    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):

    clipboard_edc06dbbb58fa88a8b1fc0e498bf07fd0.png

    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.

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