Frequency Distribution Calculator

A frequency distribution calculator systematically organizes and analyzes raw data by determining how often specific values occur within a dataset.

Frequency Distribution Table

Calculations:

• Class Mark (x) = (Lower Limit + Upper Limit) ÷ 2
• Frequency (f) = Number of observations in each class
• fx = Class Mark × Frequency
• Cumulative Frequency = Running total of frequencies
• Relative Frequency = (Frequency ÷ Total Frequency) × 100

Statistical Measures:

• Mean = Σ(fx) ÷ Σf = 342000 ÷ 50 = 6840 steps
• Mode Class = 6001-8000 (highest frequency: 20)
• Median Class = 6001-8000 (contains 25th observation)

Frequency Distribution Formula

The relative frequency is determined by dividing the category frequency by the total observations:

Relative Frequency = (Category Frequency ÷ Total Observations) × 100%

The cumulative frequency represents the running total of frequencies up to each class interval:

Cumulative Frequency = Sum of all frequencies up to and including the current class

Daily Coffee Consumption In a workplace survey tracking daily coffee consumption:

• 2 cups: 15 employees (frequency count)
• 3 cups: 25 employees (modal class)
• 4 cups: 10 employees (frequency count) Total population: 50

Relative frequencies:

• 2 cups: (15/50) × 100 = 30% (proportion)
• 3 cups: (25/50) × 100 = 50% (majority share)
• 4 cups: (10/50) × 100 = 20% (minority share)

Monthly Savings Habits Among 200 participants:

• $0-100: 80 people (lower bracket)
• $101-200: 70 people (middle bracket)
• $201-300: 50 people (upper bracket)

Cumulative frequencies:

• $0-100: 80 (first interval)
• $101-200: 150 (second interval)
• $201-300: 200 (final interval)

How to calculate mean of frequency distribution?

The weighted average approach determines the mean value using:

Mean = Σ(midpoint × frequency) ÷ Σ(frequency)

Analyzing student heights:

• 160-165 cm (8 students): midpoint 162.5
• 166-170 cm (12 students): midpoint 168
• 171-175 cm (5 students): midpoint 173

Mean calculation: [(162.5 × 8) + (168 × 12) + (173 × 5)] ÷ 25 = 167.2 cm

What is Frequency Distribution

Frequency distribution fundamentally represents a structured arrangement of data showing the number of observations falling into each category or class interval. This organizational method transforms raw data into actionable insights, enabling pattern recognition and trend analysis across various fields from market research to scientific studies.