Frequency Distribution

A frequency distribution summarizes how often values or ranges of values occur in a dataset. It organizes raw data into a format that makes patterns, central tendencies, spread, and outliers easier to see and analyze.

Definition

A frequency distribution is a table or chart that shows the number (frequency) of observations within specified intervals (classes). It can be presented as a frequency table, histogram, or bar chart.

How it works

• Frequency: count of observations that fall into a particular class or value.
• Distribution: the overall pattern of those frequencies across classes.
• Intervals (classes) must be mutually exclusive (no overlap) and exhaustive (cover all observations).
• Choice of interval size (class width) affects how much detail the distribution reveals.

Steps to construct a frequency distribution

1. Determine the range: max value − min value.
2. Choose the number of classes (k) based on the level of detail desired.
3. Calculate class width ≈ (range / k), then round up to a convenient value.
4. Define class boundaries so they don’t overlap and cover all data.
5. Tally the observations in each class to get frequencies.
6. (Optional) Compute relative frequency = frequency / total observations, and cumulative frequencies.

Visual representation

• Histogram: adjacent bars where height = frequency; useful for continuous data and for spotting shapes (normal, skewed, bimodal).
• Bar chart: separate bars, typically for categorical or discrete data.
• Frequency table: lists classes with their frequencies, relative frequencies, and cumulative totals.

A histogram often reveals a normal distribution when most observations cluster near the center and taper off symmetrically toward the tails.

Common types of frequency distributions

• Ungrouped frequency distribution: lists frequencies for each distinct value (best for small-range discrete data).
• Grouped frequency distribution: groups values into intervals (used for continuous or large-range data).
• Cumulative frequency distribution: running total of frequencies up to each class.
• Relative frequency distribution: frequencies expressed as proportions or percentages.
• Relative cumulative frequency distribution: cumulative proportions or percentages.

Example

Measuring the heights of 50 children:
– Range = tallest − shortest.
– Decide, for example, 5 classes → class width = ceil(range / 5).
– Create five non-overlapping height intervals and count how many children fall in each.
– Display counts in a table or histogram to visualize where most heights concentrate.

Use in trading

Frequency concepts appear in some trading tools:
– Point-and-figure charts (an early form of frequency/price visualization) use Xs and Os to mark price changes and filter noise.
– Traders interpret patterns such as a column of three Xs as evidence of an uptrend (demand > supply) and three Os as a downtrend (supply > demand).
– More broadly, frequency distributions can help assess price behavior, volatility, and the likelihood of outcomes when analyzing returns.

Importance and applications

Frequency distributions:
– Organize large datasets into interpretable formats.
– Reveal trends, central tendency, variability, and outliers.
– Support decision making in fields like business (sales, surveys), statistics (demographics), and finance (asset performance, risk assessment).

Key takeaways

• A frequency distribution converts raw data into counts or proportions by class.
• Proper class selection (mutually exclusive and exhaustive) is essential.
• Visual forms (histograms, tables) make underlying patterns easy to spot.
• Variants (grouped, cumulative, relative) serve different analytical needs.