Frequency Distribution Tool

What is a Frequency Distribution?

A frequency distribution shows how often each value (or range of values) occurs in a dataset. It's one of the most fundamental ways to summarize and visualize data.

Types of Frequency Distributions

Key Terms

• Frequency (f): Number of times a value/class occurs
• Relative Frequency: f / n (proportion as decimal)
• Percentage: Relative frequency × 100%
• Cumulative Frequency: Running total of frequencies
• Cumulative %: Running total of percentages
• Class Width: Range of values in each group
• Class Midpoint: Middle value of a class interval

Creating Grouped Frequency Distribution

1. Determine number of classes: Typically 5-15 (Sturges' Rule: k ≈ 1 + 3.322 log₁₀(n))
2. Calculate class width: (Max - Min) / Number of classes
3. Round up class width to convenient number
4. Start with minimum or slightly below
5. Create intervals: Non-overlapping, equal width
6. Tally frequencies: Count data points in each class

Example: Discrete Distribution

Survey ratings: [3, 5, 4, 3, 5, 4, 5, 3, 4, 4]

Rating	Frequency	Relative	%
3	3	0.30	30%
4	4	0.40	40%
5	3	0.30	30%
Total	10	1.00	100%

Example: Grouped Distribution

Test scores: [67, 72, 85, 91, 78, 88, 95, 73, 81, 69]

Class	Frequency	%	Cumulative %
60-69	2	20%	20%
70-79	3	30%	50%
80-89	3	30%	80%
90-99	2	20%	100%

Histogram

A histogram is a graphical representation of a frequency distribution:

• X-axis: Values or class intervals
• Y-axis: Frequency (count or percentage)
• Bars touch (continuous data) or separated (discrete)
• Bar height represents frequency

Distribution Shapes

• Normal (Bell-shaped): Symmetric, most common
• Skewed Right: Long tail to the right
• Skewed Left: Long tail to the left
• Uniform: All frequencies roughly equal
• Bimodal: Two peaks
• Multimodal: Multiple peaks

Applications

• Education: Grade distributions, test score analysis
• Business: Sales patterns, customer demographics
• Healthcare: Patient age distributions, treatment outcomes
• Quality Control: Defect rates, measurement distributions
• Social Science: Survey response patterns
• Economics: Income distribution, price ranges

Choosing Number of Classes

• Sturges' Rule: k = 1 + 3.322 log₁₀(n)
• Square Root Rule: k = √n
• Rice Rule: k = 2n^(1/3)
• Practical: Use 5-15 classes depending on data

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