STATISTICSDescriptive StatisticsStatistics Calculator
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Frequency Distribution Calculator

Free frequency distribution calculator. Build frequency tables, class boundaries, midpoints, relativ

Run CalculatorExplore data analysis and statistical calculations

Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

๐Ÿ“Š
STATISTICSDescriptive Statistics

Frequency Distribution โ€” Build Frequency Tables

Build frequency tables: absolute, relative, cumulative frequencies. Auto-bins with Sturges' rule or custom class intervals.

Real-World Scenarios โ€” Click to Load

freq_dist_results.sh
CALCULATED
Total (n)
20
Classes (k)
6
Class Width
3.8333
Range
72.00 โ€“ 95.00
Share:
Frequency Distribution Result
n = 20 values
k = 6
Width: 3.8333Range: 72.00 โ€“ 95.00
numbervibe.com/calculators/statistics/frequency-distribution-calculator
ClassMidpointfRelativeCumulativeCum. Rel.%
72.00 โ€“ 75.8373.9220.100020.100010.00%
75.83 โ€“ 79.6777.7530.150050.250015.00%
79.67 โ€“ 83.5081.5840.200090.450020.00%
83.50 โ€“ 87.3385.4240.2000130.650020.00%
87.33 โ€“ 91.1789.2540.2000170.850020.00%
91.17 โ€“ 95.0093.0830.1500201.000015.00%

Calculation Breakdown

COMPUTATION
Sample size (n)
20
ext{Count} ext{of} ext{data} ext{points}
COMPUTATION
Range
23.0000
max โˆ’ min = 95 โˆ’ 72
BINNING
Sturges' k
6
โŒˆ1 + 3.322 imes log_{1}_{0}(n)โŒ‰
BINNING
Class width
3.8333
R/k = 23.00/6
Number of classes
6
ext{Classes} ext{used}
VERIFICATION
Relative freq sum
1.0000
\text{Sigma} (f/n) = 1

Frequency Bar Chart

Cumulative Frequency Ogive

Relative Frequency Chart

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • โ€ข Frequency (f): count of values in each class interval
  • โ€ข Relative frequency: f/n โ€” proportion of data in each class
  • โ€ข Cumulative frequency: running total โ€” shows how many values fall at or below each upper bound
  • โ€ข Sturges' rule: k = โŒˆ1 + 3.322 ร— logโ‚โ‚€(n)โŒ‰ for auto-binning

Did You Know?

๐Ÿ“ŠA frequency distribution summarizes raw data into classes, making patterns visible.Source: NIST
๐Ÿ“Sturges' rule (1926) suggests k = 1 + 3.322ร—logโ‚โ‚€(n) classes. For n=100, that gives about 8 classes.Source: Wikipedia
๐Ÿ“ˆThe cumulative frequency ogive is an S-shaped curve. Its slope indicates where data is concentrated.Source: Wolfram MathWorld
๐ŸŽฏClass boundaries should not overlap. Use [a, b), [b, c) โ€” left-inclusive, right-exclusive.Source: Statistical best practices

How Frequency Distributions Work

A frequency distribution organizes raw data into class intervals and counts how many values fall in each.

Step 1: Choose Class Intervals

Use auto (Sturges' rule) or specify number of classes or class width.

Step 2: Count Frequencies

For each class, count data points. f = count. Relative = f/n. Cumulative = running sum of f.

Frequency Types Compared

TypeFormulaUse
Absolute (f)Count in classRaw counts
Relativef / nProportions; sum = 1
CumulativeRunning sum of fOgive; percentiles
PercentageRelative ร— 100Easy interpretation

Frequently Asked Questions

What is Sturges' rule?

Sturges' rule gives k = ceil(1 + 3.322ร—log10(n)) classes. It's a heuristic for choosing the number of bins.

What is the difference between frequency and relative frequency?

Frequency is the raw count. Relative frequency = count/total, so it sums to 1.

What is a cumulative frequency ogive?

A line graph of upper class boundaries vs cumulative frequency. S-shaped.

Frequency Distribution at a Glance

f
Absolute frequency
f/n
Relative frequency
ฮฃf
Cumulative
mid
(L+U)/2

Disclaimer: Sturges' rule is a guideline. For skewed or multimodal data, consider Freedman-Diaconis or custom binning.

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