Relative Frequency Calculator
Print Page| Category | Frequency (f) | Relative Frequency (decimal) | Relative Frequency (%) | Cumulative Relative Frequency (%) |
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A Relative Frequency Calculator (also known as a Relative Frequency Table Calculator, Percentage Frequency Generator, Absolute Count to Proportion Converter, or Empirical Probability Distribution Analyzer) converts raw frequency counts (fi) into exact relative frequencies (rfi = fi ÷ n), percentage shares (%i = [fi ÷ n] · 100), cumulative relative frequencies (crfi = ∑ rfj), and empirical event probabilities.
In market research surveys, customer satisfaction CSAT scoring, medical clinical trial outcomes, and quality control defect sorting, relative frequency normalizes raw sample sizes into comparable proportions that sum to 1.00 (or 100%).
Our free online Relative Frequency Calculator provides instant calculations across all frequency parameters:
- Total Sample Size Constraint (n):
n = ∑ fi(Sum of all absolute frequencies). - Relative Frequency Formula (rfi):
rfi = fi ÷ n(where∑ rfi = 1.0000). - Percentage Frequency Formula (%i):
%i = rfi · 100 = ( fi ÷ n ) · 100(where∑ %i = 100.00%). - Cumulative Relative Frequency (crfi):
crfi = ∑j=1i rfj = cfi ÷ n. - Empirical Frequentist Probability Estimate P(A):
P(A) ≈ Relative Frequency(A) = &lim;n → &infty; ( fA ÷ n ).
Master Relative Frequency Reference Table (Customer CSAT Ratings: n = 200 Responses)
The table below displays raw counts (fi), relative frequencies (rfi), percentage shares (%i), cumulative frequencies (cfi), and cumulative relative frequencies (crfi) for 200 customer feedback ratings (n = 200 total responses):
| CSAT Star Rating Category | Raw Count (fi) | Relative Frequency (rfi = f/200) | Percentage Share (%) | Cumulative Count (cfi) | Cumulative Relative Frequency (crfi) |
|---|---|---|---|---|---|
| 5 Stars (Excellent Service) | 90 reviews | 0.4500 | 45.00% | 90 | 0.4500 (45.0%) |
| 4 Stars (Good Service) | 60 reviews | 0.3000 | 30.00% | 150 | 0.7500 (75.0% Satisfied) |
| 3 Stars (Average Service) | 30 reviews | 0.1500 | 15.00% | 180 | 0.9000 (90.0%) |
| 2 Stars (Poor Service) | 12 reviews | 0.0600 | 6.00% | 192 | 0.9600 (96.0%) |
| 1 Star (Terrible Service) | 8 reviews | 0.0400 | 4.00% | 200 (Total) | 1.0000 (100.0% Complete) |
Step-by-Step Customer Review Relative Frequency Calculation
To analyze a customer feedback dataset with n = 200 total responses:
Step 1 (Calculate Sample Size n): n = 90 + 60 + 30 + 12 + 8 = 200 total reviews
Step 2 (Calculate 5-Star Relative Frequency rf_1): rf1 = 90 ÷ 200 = 0.4500 &implies; %1 = 0.4500 · 100 = 45.00%
Step 3 (Calculate 4-Star Relative Frequency rf_2): rf2 = 60 ÷ 200 = 0.3000 &implies; %2 = 0.3000 · 100 = 30.00%
Step 4 (Calculate Cumulative Satisfied Rating [4 or 5 Stars]): crf2 = rf1 + rf2 = 0.4500 + 0.3000 = 0.7500 &implies; 75.00% Satisfied Customers
Step 5 (Verify Sum of Relative Frequencies): 0.4500 + 0.3000 + 0.1500 + 0.0600 + 0.0400 = 1.0000 (100.0% Total)
Thus, 45% of customers gave a 5-star rating, and 75% of all customers gave a positive rating (4 or 5 stars).
Frequency Metrics Comparison: Relative vs. Absolute vs. Cumulative
Below is a comparative reference chart detailing when to use Relative Frequency versus related statistical measures:
| Frequency Metric Type | Mathematical Definition | Sum / Total Constraint | Primary Practical Application |
|---|---|---|---|
| Relative Frequency (rfi) | rfi = fi ÷ n (Proportion of total) | Must sum to EXACTLY 1.00 (or 100%) | Comparing datasets with different sample sizes. |
| Absolute Frequency (fi) | Raw integer count of observed items | Sums to total sample size n | Recording initial raw survey responses or counts. |
| Cumulative Relative Frequency (crfi) | Running total sum of proportions ∑ rfj | Final category equals 1.00 (100%) | Percentile rankings and ogive graph plotting. |
History & Mathematics: 1662 John Graunt to 1920s Richard von Mises
1662 John Graunt & Mortality Table Proportions
In 1662, English haberdasher and pioneer statistician John Graunt published Natural and Political Observations Made upon the Bills of Mortality, creating the world’s first life tables by converting raw death counts into relative frequency proportions of mortality.
1920s Richard von Mises & Frequentist Probability Definition
In the 1920s, Austrian mathematician Richard von Mises established the Frequentist Definition of Probability, defining event probability as the limiting long-run relative frequency of occurrence in infinitely repeated trials P(A) = &lim;n → &infty; (fA ÷ n).
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Frequently Asked Questions (FAQ)
How do you calculate Relative Frequency?
Divide the category count fi by the total sample size n (rfi = fi ÷ n).
How do you convert Relative Frequency to a Percentage?
Multiply the relative frequency proportion by 100 (%i = rfi · 100).
Why do all Relative Frequencies in a table sum to 1.0?
Because relative frequencies represent parts of a single complete whole, their combined sum must always equal 1.00 (or 100%).