Quartile Deviation – Formula, Calculation & Interpretation 📘📉
Quartile Deviation (Q.D.), also known as the Semi-Interquartile Range, measures the spread of the middle 50% of a dataset.
It is less affected by extreme values and is particularly useful for skewed distributions.
1. Definition
Quartile Deviation is half of the difference between the third quartile (Q3) and the first quartile (Q1).
Formula
Q.D. = (Q3 – Q1) / 2
Coefficient of Quartile Deviation
Coefficient of Q.D. = (Q3 – Q1) / (Q3 + Q1)
Key InsightQuartile Deviation ignores extremes and focuses on the central 50% of data, making it useful for distributions with outliers or open-ended intervals.
2. Steps to Calculate Q.D. (Grouped Data)
-
Prepare cumulative frequencies.
-
Locate:
- Q1 at ( N/4 )
- Q3 at ( 3N/4 )
-
Identify the Q1 and Q3 classes.
-
Apply the quartile formula:
Qk = L + [( (kN/4) – C.F_prev ) / f ] × h
- Compute Q.D. and Coefficient.
3. Solved Example (Grouped Data)
Class Interval & Frequency
| Class Interval | f |
|---|---|
| 0–10 | 4 |
| 10–20 | 6 |
| 20–30 | 10 |
| 30–40 | 8 |
| 40–50 | 2 |
Total ( N = 30 )
Step 1: Find Q1
( N/4 = 30/4 = 7.5 ) → lies in class 10–20.
Values:
L = 10
C.F_prev = 4
f = 6
h = 10
Q1 = 10 + [(7.5 – 4) / 6] × 10
= 10 + (3.5/6) × 10
≈ 10 + 5.83
Q1 ≈ 15.83
Step 2: Find Q3
( 3N/4 = 90/4 = 22.5 ) → lies in class 20–30.
Values:
L = 20
C.F_prev = 10
f = 10
h = 10
Q3 = 20 + [(22.5 – 10) / 10] × 10
= 20 + (12.5/10) × 10
= 20 + 12.5
Q3 = 32.5
Step 3: Compute Q.D.
Q.D. = (Q3 – Q1) / 2
= (32.5 – 15.83) / 2
≈ 16.67 / 2
Q.D. ≈ 8.34
Step 4: Coefficient of Q.D.
Coefficient = (Q3 – Q1) / (Q3 + Q1)
= 16.67 / 48.33
≈ 0.345
4. Merits of Quartile Deviation ✔️
- Not affected by extreme values
- Simple to compute and interpret
- Useful for skewed distributions
- Works for open-ended classes
- Focuses on the central 50% of data
5. Limitations of Quartile Deviation ❌
- Ignores 50% of data (only uses Q1 and Q3)
- Not suitable for detailed analysis
- Cannot be used for algebraic operations
- Less accurate compared to Standard Deviation
Exam TipQuartile Deviation is only accurate for understanding the middle spread. For precise variability, Standard Deviation is preferred.
6. Uses in Business & Economics 📌
- Income distribution analysis
- Analyzing market demand variations
- Quality control comparisons
- Skewed data representation
- Initial risk estimation
7. Summary ✨
- Q.D. = (Q3 – Q1)/2
- Measures dispersion of middle 50%
- Good for skewed or open-ended data
- Coefficient of Q.D. is unit-free
- Not as precise as Standard Deviation
Quiz Time 🎯
Test Your Knowledge
Question 1 of 5
1. Quartile Deviation measures dispersion of: