Quartile Deviation (QD) Calculator
Use this unified calculator to find the quartile deviation (QD) for both ungrouped (raw) data and grouped (frequency distribution) data. QD measures the spread of the middle 50% of data as a relative measure.
Quick Start
| Quartile Deviation Calculator | |
|---|---|
| Data Type | Ungrouped (Raw Data) Grouped (Frequency Distribution) |
| Enter the X Values (Separated by comma,) | |
| Type of Frequency Distribution | DiscreteContinuous |
| Enter the Classes for X (Separated by comma,) | |
| Enter the frequencies (f) (Separated by comma,) | |
| Results | |
| Number of Observations (N): | |
| Ascending order of X values: | |
| First Quartile (Q₁): | |
| Second Quartile (Q₂) / Median: | |
| Third Quartile (Q₃): | |
| Quartile Deviation (QD): | |
| Coefficient of Quartile Deviation: | |
Understanding Quartile Deviation
QD measures the spread as half the interquartile range:
- QD = (Q₃ - Q₁) / 2 = IQR / 2
- Robust to outliers
- Relative measure when coefficient is used
- Represents average deviation from median
Coefficient of Quartile Deviation
$$CQD = \frac{Q_3 - Q_1}{Q_3 + Q_1}$$
This is a unitless measure ranging from 0 to 1.
Formulas
Quartile Deviation
$$QD = \frac{Q_3 - Q_1}{2}$$
Coefficient of Quartile Deviation
$$CQD = \frac{Q_3 - Q_1}{Q_3 + Q_1}$$
Where:
- Q₁ = First quartile
- Q₃ = Third quartile
Worked Examples
Example 1: Ungrouped Data
Data: 45, 52, 58, 63, 72, 81, 85, 90, 95
Q₁ = 55, Q₃ = 87.5
$$QD = \frac{87.5 - 55}{2} = \frac{32.5}{2} = 16.25$$
$$CQD = \frac{87.5 - 55}{87.5 + 55} = \frac{32.5}{142.5} = 0.228$$
Relationship to Other Measures
- QD = IQR / 2
- QD is the semi-interquartile range
- CQD provides unitless comparison
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