Frequency Distribution Calculator

A frequency distribution organizes data into bins or intervals and shows how many observations fall into each bin. This calculator creates both a frequency distribution table and visual representations including histograms and frequency polygons.

What is a Frequency Distribution?

A frequency distribution is a table or graph that displays the frequency of various outcomes in a sample. It shows how often each value or range of values occurs in your dataset. This helps you understand the shape and spread of your data at a glance.

Components of a Frequency Distribution

  • Bins (Classes): Ranges of values that group your data
  • Frequency: The count of observations in each bin
  • Relative Frequency: The percentage of total observations in each bin
  • Cumulative Frequency: The running total of frequencies
  • Midpoint: The center point of each bin (used for frequency polygons)

Visualization Options

  • Histogram: Bar chart showing frequencies with no gaps between bars
  • Frequency Polygon: Line graph connecting the midpoints of each bin
  • Both: Display histogram and frequency polygon together

When to Use Frequency Distributions

  • To summarize large datasets in a compact form
  • To visualize the distribution shape (normal, skewed, uniform, bimodal)
  • To identify patterns, gaps, or outliers in your data
  • To prepare data for statistical analysis
  • To communicate findings in reports and presentations

Bin Calculation Methods

  • Sturges' Rule (Auto): Calculates optimal bin count as 1 + 3.322 log(n)
  • Manual Bin Count: Specify the exact number of bins you want
  • Custom Bin Width: Set a specific width for each bin

Interpreting Your Results

  • Normal Distribution: Bell-shaped curve with mean ≈ median ≈ mode
  • Skewed Right: Tail extends to the right; mean > median
  • Skewed Left: Tail extends to the left; mean < median
  • Bimodal: Two distinct peaks suggest two underlying groups
  • Uniform: Roughly equal frequencies across all bins