✓ Commas · spaces · line breaks · decimals · large datasets supportedn = 0
⚙️ Grouping Options
⊞ Custom Class Intervals
Define your own class boundaries. Each class is [Lower, Upper) — open on the right — except the last which is [Lower, Upper] closed.
Classes must be added in ascending order (each class starts where the previous one ends).
➕ Add a Class
Enter the lower and upper boundary for your first class, then keep adding classes in ascending order.
📋 Defined Classes
No classes defined yet.
Ungrouped Results
📤 Export & Copy:
📈 Distribution Shape & Character
Frequency Histogram
Bars = observed; red dashed = fitted normal curve; teal line = mean
Vertical Boxplot
Five-number summary + outliers (red dots) + mean (amber dot)
📊 Full Descriptive Statistics — Raw Data
Statistic
Value
Economic & Statistical Interpretation
Grouped Results
🗂 Grouping Summary
📋 Frequency Distribution Table
Class Interval
Lower (L)
Upper (U)
Midpoint (mᵢ)
Freq (fᵢ)
Rel Freq
Rel %
Cum Freq
Cum %
fᵢ·mᵢ
fᵢ·mᵢ²
★ Modal class (highest frequency) highlighted in teal. Last class uses closed bracket [L, U].
Frequency Histogram
∑ Grouped Descriptive Statistics
Statistic
Value
Economic & Statistical Interpretation
⇄ Ungrouped vs Grouped Comparison
Statistic
Ungrouped (exact)
Grouped (approx.)
|Difference|
Grouped statistics use class midpoints as value proxies — information is lost in the grouping process. Smaller class width (larger k) reduces approximation error. Use ungrouped statistics for precise analysis; grouped for frequency pattern identification.
