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Frequency Distribution

Updated 01 Oct 2026

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What it is
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  a table showing values or classes and their observed frequencies
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  a grouped frequency distribution uses intervals
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Guidelines for constructing one
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  decide the number of classes (typically 5–20)
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  determine the class width
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  determine the class limits
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  tally each data point into its class
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  count the tallies to get each class's frequency
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Sturges' rule
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  $k\approx1+\log_2 n\approx1+3.322\log_{10}n$
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  a heuristic starting point, not a requirement that guarantees a useful grouping
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Checks
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  classes must not overlap
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  every observation must fit a class
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  $\sum_i f_i=n$
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Example
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  the vehicle-price example has seven class frequencies: $8,23,17,18,8,4,2$ , totaling $80$ .
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  relative frequencies: $0.10,0.2875,0.2125,0.225,0.10,0.05,0.025$ .
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  cumulative frequencies: $8,31,48,66,74,78,80$ .
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Class selection
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  rules such as $2^k>n$ or Sturges’ rule are starting heuristics, not uniquely correct answers.
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  for $n=80$ , $2^7>80$ . The observed range divided by seven is about $2911.29$ , motivating a convenient class width of $3000$ in the slide example.
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Related

Linked references 11

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