How to Calculate Cumulative Relative Frequency

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When a statistician or scientist compiles a data set, an important characteristic is the frequency of each measurement or answer to a survey question. This is simply the number of times this item appears in the set. When you compile the results in an ordered table, the cumulative frequency of each data item is the sum of the frequencies of all the items that come before it. In some cases, analysis of the data may require establishing the relative frequency for each data item, which is the frequency of each item divided by the total number of measurements or respondents. The cumulative relative frequency of each data item is then the sum of the relative frequencies of all the items that precede it added to the relative frequency of that item.

TL;DR (Too Long; Didn't Read)

When analyzing, the frequency of each item is the number of times it occurs, and the relative frequency is the frequency divided by the total number of measurements. If you tabulate the data, the cumulative relative frequency for each item is the relative frequency for that item added to the relative frequencies of all the items that come before it.

Calculating Relative Cumulative Frequency

Because cumulative relative frequency depends not only on the number of incidences of each measurement or response, but also on the values of those responses in relation to each other, it's standard practice to construct a table of observations. Once you have entered the data items in the first column, you use simple arithmetic to fill out the other columns.

  1. Construct the Table

  2. The table has four columns. The first is for the data results, and the second is for the frequency of each result. In the third, you list the relative frequencies, and in the fourth, the cumulative relative frequencies. Note that the sum of frequencies in the second column equals the total number of measurements or responses and the sum of relative frequencies in the third column equals one or 100 percent, depending on whether you calculate them as fractions or percentages. The cumulative relative frequency of the last data item in the table is one or 100 percent.

  3. List the Measurements or Responses in the First Column

  4. The data in this column may be numbers or ranges of numbers. For example, in a study of heights of soccer players, each entry may be a particular height or a range of heights. Each entry establishes a row in the table.

  5. Put Frequencies in the Second Column

  6. The frequency of each data item is simply the number of times it appears in the data set.

  7. Calculate Relative Frequencies in the Third Column

  8. The relative frequency for each data item is the frequency of that item divided by the total number of observations. You can express this number as a fraction or a percentage.

  9. Sum Cumulative Relative Frequencies in the Fourth Column

  10. The cumulative relative frequency for each data item is the sum of the relative frequencies of all the items that come before it added to the relative frequency for that item. For example, the cumulative relative frequency of the third item is the sum of the relative frequencies of that item and the relative frequencies of item one and item two.

References

About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010 with the goal of exploring scientific, cultural and practical topics, and at last count had reached over a hundred million readers through various sites.

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