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Frequency Distribution Tables

📑 5 slides 👁 1 views 📅 11/3/2026 📺 YouTube
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Make Raw Data Readable

A frequency distribution table (FDT) organizes responses into categories or intervals and counts how often each occurs.

Make Raw Data Readable
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Choose the Right Table Type

  • Use an ungrouped FDT for categories or a small set of distinct values, such as favorite snacks or colors.
  • Use a grouped FDT for numerical data with many observations, organizing values into class intervals or ranges.
  • A survey of favorite snacks can list each snack separately; quiz scores are better summarized in score ranges.
  • Decide by asking whether the data are categorical or numerical and whether there are many unique values.
Choose the Right Table Type
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Build an Ungrouped FDT

  • For 15 classmates' favorite primary colors, create columns for category, tally, and frequency.
  • List each category once, then scan every response and add a tally mark to its matching category.
  • Bundle tallies in groups of five to make counting easier; count each category's marks to find its frequency.
  • Example result: red appears 5 times, blue 7 times, and yellow 3 times; the frequencies sum to 15.
Build an Ungrouped FDT
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Create Grouped and Extended Tables

  • For 30 quiz scores from 30 to 49, the range is 49 minus 30, which equals 19.
  • Choose five classes; divide the range by five to get 3.8, then round the class width up to 4.
  • Create five non-overlapping intervals of width four, such as 30–33, 34–37, 38–41, 42–45, and 46–50.
  • Tally each score into one interval; cumulative frequency is a running total, while relative frequency is class frequency divided by 30.
Create Grouped and Extended Tables
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Interpret and Use the Results

  • Check that all category or interval frequencies add up to the total number of observations in the data set.
  • Relative frequency expresses each count as a share of the total; multiply by 100 to convert it to a percentage.
  • In a snack survey with 15 responses, a category with frequency 7 has relative frequency 7/15, about 47%.
  • FDTs reveal patterns and prepare data for graphs and further analysis, including measures of center and variation.
Interpret and Use the Results
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