Frequency Distribution Table
Print Page| Class Interval | Class Midpoint (x_m) | Frequency (f) | Relative Frequency (%) | Cumulative Frequency |
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A Frequency Distribution Calculator (also known as a Frequency Table Calculator, Relative & Cumulative Frequency Generator, Grouped Data Table Utility, or Ogive Curve Analyzer) organizes raw quantitative data into structured frequency distribution tables, computing class counts (K = 1 + 3.322 · log10n), absolute frequencies (fi), relative frequencies (rfi = fi ÷ n), percentage frequencies (%i = rfi · 100), cumulative frequencies (cfi = ∑ f), and class midpoints (xm).
Frequency distribution tables form the foundational backbone of descriptive statistics. By compressing large unstructured datasets into ordered bin intervals, frequency tables make central tendency, dispersion, modal peaks, and cumulative distributions immediately readable.
Our free online Frequency Distribution Calculator provides instant calculations across all frequency metrics:
- Absolute Frequency Sum Constraint:
∑ fi = n(The sum of all class frequencies equals total sample size). - Relative Frequency (rfi):
rfi = fi ÷ n(where∑ rfi = 1.000). - Percentage Frequency (%i):
%i = ( fi ÷ n ) · 100. - Cumulative Frequency (cfi):
cfi = cfi-1 + fi(Running total of observations). - Relative Cumulative Frequency (rcfi):
rcfi = cfi ÷ n. - Class Midpoint (xm,i):
xm,i = ( Lower Limit + Upper Limit ) ÷ 2. - Grouped Sample Mean Estimate (&x̄;grouped):
&x̄;grouped = ∑ ( fi · xm,i ) ÷ n.
Master Grouped Frequency Distribution Reference Table (n = 50 Call Center Calls)
The table below displays class limits, class midpoints (xm), absolute frequencies (f), relative frequencies (rf), percentage distributions, and cumulative frequencies (cf) for a 50-call support duration dataset (Range = 1.2 to 24.8 minutes):
| Class Interval (Minutes) | Class Midpoint (xm) | Absolute Frequency (f) | Relative Frequency (rf) | Percentage Frequency (%) | Cumulative Frequency (cf) | Relative Cumulative (rcf) |
|---|---|---|---|---|---|---|
| 1.0 to 4.9 min | 2.95 min | 12 Calls | 0.240 | 24.00% | 12 Calls | 24.00% |
| 5.0 to 8.9 min (Modal Bin) | 6.95 min | 18 Calls (Peak) | 0.360 | 36.00% | 30 Calls (60%) | 60.00% |
| 9.0 to 12.9 min | 10.95 min | 10 Calls | 0.200 | 20.00% | 40 Calls (80%) | 80.00% |
| 13.0 to 16.9 min | 14.95 min | 5 Calls | 0.100 | 10.00% | 45 Calls | 90.00% |
| 17.0 to 20.9 min | 18.95 min | 3 Calls | 0.060 | 6.00% | 48 Calls | 96.00% |
| 21.0 to 24.9 min | 22.95 min | 2 Calls | 0.040 | 4.00% | 50 Calls (100%) | 100.00% |
Step-by-Step Grouped Mean Calculation (&x̄;grouped)
To estimate the sample mean from the 50-call grouped frequency table:
Step 1 (Multiply f · x_m for each bin):
- Bin 1: 12 · 2.95 = 35.40
- Bin 2: 18 · 6.95 = 125.10
- Bin 3: 10 · 10.95 = 109.50
- Bin 4: 5 · 14.95 = 74.75
- Bin 5: 3 · 18.95 = 56.85
- Bin 6: 2 · 22.95 = 45.90
Step 2 (Sum Products ∑[f · x_m]): 35.40 + 125.10 + 109.50 + 74.75 + 56.85 + 45.90 = 447.50
Step 3 (Divide by Total Sample Size n = 50): &x̄;grouped = 447.50 ÷ 50 = 8.95 minutes
Thus, the grouped mean call duration is 8.95 minutes, with 60% of all calls lasting less than 8.9 minutes.
Frequency Table Types: Ungrouped vs. Grouped vs. Cumulative Ogive
Below is a comparative reference chart detailing the three primary formats for frequency distribution tables:
| Frequency Table Format | Data Value Grouping Method | Primary Visual Graphical Output | Best Dataset Condition |
|---|---|---|---|
| Ungrouped Frequency Table | Lists every distinct raw value individually. | Bar Chart / Dot Plot | Discrete data with few distinct values. |
| Grouped Frequency Table | Bins data into equal interval classes. | Histogram / Frequency Polygon | Continuous data with wide ranges. |
| Cumulative Ogive Table | Accumulates running totals (cf and rcf). | Ogive Curve (S-Shaped Graph) | Percentile ranking & threshold cutoffs. |
History & Mathematics: 1662 John Graunt to 1895 Karl Pearson
1662 John Graunt & Mortality Tables
In 1662, London merchant John Graunt published Natural and Political Observations Made upon the Bills of Mortality, constructing the first empirical mortality frequency distribution tables in history and founding demography.
1895 Karl Pearson & Frequency Curves
In 1895, English mathematician Karl Pearson published his systematic classification of continuous frequency curves in Philosophical Transactions of the Royal Society.
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Frequently Asked Questions (FAQ)
What is a Frequency Distribution?
A frequency distribution is a statistical table that displays the number of times each distinct data value or class interval occurs in a dataset.
How do you calculate Relative Frequency?
Divide the absolute class frequency f by the total sample size n (rf = f ÷ n).
What is Cumulative Frequency?
Cumulative frequency is the running total of all class frequencies up to and including the current class interval (cfi = ∑ f).