Quartile Deviation Calculator
Calculate Quartile Deviation ($\text{QD} = \frac{Q_3 - Q_1}{2}$), Semi-Interquartile Range, Coefficient of Quartile Deviation, and Interquartile Range (IQR).
Calculate Quartile Deviation & Semi-IQR
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Calculation Results
Calculated using semi-interquartile dispersion equations: \text{QD} = \frac{Q_3 - Q_1}{2}, \quad \text{Coeff of QD} = \frac{Q_3 - Q_1}{Q_3 + Q_1}
Quick Summary
The Quartile Deviation Calculator evaluates Semi-Interquartile Range ($\text{QD} = \frac{Q_3 - Q_1}{2}$), Coefficient of Quartile Deviation, $Q_1$, $Q_3$, and Interquartile Range (IQR).
Formula Explanation
\text{Quartile Deviation QD} = \frac{Q_3 - Q_1}{2}
\text{Coefficient of QD} = \frac{Q_3 - Q_1}{Q_3 + Q_1}How It Works
Quartile deviation (also called semi-interquartile range) is half the distance between the 75th percentile ($Q_3$) and 25th percentile ($Q_1$). The Quartile Deviation Calculator sorts your dataset, computes quartiles, and calculates absolute and relative quartile deviation metrics.
Step-by-Step Worked Example
Practical Problem: Calculate quartile deviation for dataset: 10, 15, 20, 25, 30, 35, 40, 45 ($n = 8$).
- Step 1: Calculate $Q_1$ (25th percentile): $Q_1 = \mathbf{16.2500}$.
- Step 2: Calculate $Q_3$ (75th percentile): $Q_3 = \mathbf{38.7500}$.
- Step 3: Calculate Interquartile Range ($\text{IQR}$): $38.75 - 16.25 = \mathbf{22.5000}$.
- Step 4: Divide IQR by 2 for Quartile Deviation ($\text{QD}$): $22.50 / 2 = \mathbf{11.2500\text{ Quartile Deviation}}$.
- Step 5: Calculate Coefficient of QD: $(38.75 - 16.25) / (38.75 + 16.25) = 22.50 / 55.00 = \mathbf{0.4091}$.
Real-World Calculation Examples
Scenario 1: 8-Item Dataset (10 to 45)
Parameters: n = 8
Result: Quartile Deviation 11.2500 (IQR 22.5000).
Scenario 2: Skewed Salary Data (Q1 $40k, Q3 $100k)
Parameters: Q1 $40k, Q3 $100k
Result: QD $30,000 (Semi-IQR spread).
Scenario 3: Symmetrical Test Scores (Q1 70, Q3 90)
Parameters: Q1 70, Q3 90
Result: QD 10.00 points (IQR 20.00 points).
Scenario 4: Coefficient of QD Relative Comparison
Parameters: Q1 15, Q3 45
Result: Coeff of QD 0.5000.
Key Benefits of Using This Calculator
Outlier Resistant Dispersion
Provides a measure of dispersion unaffected by extreme tail values.
Coefficient of Quartile Deviation
Computes relative dimensionless quartile deviation for comparing datasets.
Full Quartile Summary
Displays $Q_1$, $Q_2$ (Median), $Q_3$, and IQR.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is quartile deviation?
Quartile deviation (semi-interquartile range) is half the difference between the third and first quartiles ($\text{QD} = \frac{Q_3 - Q_1}{2}$).
Why use quartile deviation instead of standard deviation?
Quartile deviation is preferred for skewed distributions with extreme outliers because it depends strictly on the middle 50% of data.
What is Coefficient of Quartile Deviation?
Coefficient of QD is $\frac{Q_3 - Q_1}{Q_3 + Q_1}$, a relative dimensionless measure of quartile dispersion.
What is relationship between QD and IQR?
Quartile deviation is exactly half of the Interquartile Range ($\text{QD} = \text{IQR} / 2$).
In a normal distribution, how does QD relate to standard deviation ($\sigma$)?
For a normal bell curve, $\text{QD} \approx 0.6745 \cdot \sigma$.
Can quartile deviation be zero?
Yes — if $Q_3 = Q_1$ (e.g. more than 50% of data points are identical), $\text{QD} = 0$.
Can quartile deviation be negative?
No — since $Q_3 \ge Q_1$, quartile deviation is always non-negative ($\ge 0$).
What is mean deviation vs quartile deviation?
Mean deviation averages absolute deviations from the mean; quartile deviation measures half-spread between $Q_3$ and $Q_1$.
How do I calculate QD in Excel?
Use formula =(QUARTILE(range, 3) - QUARTILE(range, 1)) / 2.
When is QD best utilized in data analysis?
QD is best used when data is open-ended at extremes or when median is reported as central tendency.