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Frequency Distributions Overview

Aug 21, 2025

Overview

This lecture covers frequency distributions, including definitions of frequency, relative frequency, and cumulative frequency, and demonstrates how to calculate and interpret them using examples.

Frequency Distributions

  • A frequency distribution lists each category of data and the number of times it occurs (frequency).
  • Frequency distributions apply to both qualitative (categories) and quantitative (numerical) data.

Relative Frequency

  • Relative frequency is the ratio of a category's frequency to the total number of outcomes.
  • Calculate relative frequency by dividing each frequency by the total sample size.
  • Relative frequency can be expressed as a fraction, decimal, or percent.

Cumulative Relative Frequency

  • Cumulative relative frequency is the running total of relative frequencies as you move through the categories.
  • Add each new relative frequency to the sum of the previous relative frequencies.
  • The cumulative relative frequency should be close to 1 (or 100%) when all categories are included.

Example: Blood Type Data

  • Sample size: 30 patients' blood types observed (O, A, B, AB).
  • Frequencies: O = 11, A = 11, B = 5, AB = 3.
  • Relative frequencies: O = 0.37, A = 0.37, B = 0.17, AB = 0.10.
  • Cumulative relative frequencies: 0.37, 0.74, 0.91, 1.01 (rounding may cause slight deviation from 1).

Example: Number of TVs in Households

  • Sample size: 40 households, TVs per household recorded (0, 1, 2, 3, 4, 5).
  • Frequencies: 0 TVs = 1, 1 TV = 14, 2 TVs = 14, 3 TVs = 8, 4 TVs = 2, 5 TVs = 1.
  • Relative frequencies: 0 TVs = 0.025, 1 TV = 0.35, 2 TVs = 0.35, 3 TVs = 0.20, 4 TVs = 0.05, 5 TVs = 0.025.
  • For 4 or more TVs: add relative frequencies for 4 and 5 TVs (0.05 + 0.025 = 0.075 or 7.5%).

Key Terms & Definitions

  • Frequency — Number of times a value or category occurs in a data set.
  • Relative Frequency — Frequency divided by total outcomes; shown as decimal, fraction, or percent.
  • Cumulative Relative Frequency — Running total of relative frequencies up to a certain category.
  • Discrete Data — Data that can only take certain distinct values (e.g., number of TVs, cannot be 2.5).

Action Items / Next Steps

  • Prepare a table including frequency, relative frequency, and cumulative relative frequency for homework data sets.

Full transcript