This article discusses Quartile Deviation, also known as the Interquartile Range (IQR), a measure of dispersion that focuses on the spread of the middle 50% of data. It is especially useful when data is skewed or contains outliers.
What is Quartile Deviation?
Quartile Deviation measures the dispersion by considering the distance between the first and third quartiles. It helps understand how data is spread around the median.
Key Terms
- Q1 (First Quartile): Value below which 25% of the data lies.
- Q3 (Third Quartile): Value below which 75% of the data lies.
- Median (Q2): Middle value of the dataset.
Formula
Quartile Deviation (Q.D.):
Q.D. = (Q3 − Q1) / 2
Coefficient of Quartile Deviation:
Coefficient = (Q3 − Q1) / (Q3 + Q1)
1. Example (Ungrouped Data)
Consider the following data set:
5, 7, 8, 12, 13, 15, 18, 21, 25
- Arrange the data (already sorted).
- Find Q1 (1st Quartile) = 8
- Find Q3 (3rd Quartile) = 21
Quartile Deviation: (21 − 8) / 2 = 6.5
Coefficient: (21 − 8) / (21 + 8) = 13 / 29 ≈ 0.448
2. Example (Grouped Data)
Use cumulative frequency to locate Q1 and Q3 using interpolation formulas:
Q1 formula: Q1 = L + [(N/4 − F) / f] × h
Q3 formula: Q3 = L + [(3N/4 − F) / f] × h
L= lower boundary of Q1 or Q3 classN= total frequencyF= cumulative frequency before Q1 or Q3 classf= frequency of the classh= class width
Merits of Quartile Deviation
- Simple to understand and calculate
- Not affected by extreme values or outliers
- Useful in skewed distributions
Demerits of Quartile Deviation
- Ignores 50% of the data (central 50% only considered)
- Not suitable for further mathematical treatments
- Less precise than Standard Deviation in some analyses
When to Use Quartile Deviation?
Quartile Deviation is best used when:
- Data contains outliers or is not symmetrically distributed
- A quick measure of spread around the median is needed
Practical Applications
- Income and wealth distribution studies
- Educational test scores where outliers may exist
- Health data where variability is concentrated in the middle range
Comparison
| Measure | Considers | Sensitive to Outliers | Mathematical Use |
|---|---|---|---|
| Range | Extreme values | Yes | No |
| Quartile Deviation | Middle 50% | No | Limited |
| Standard Deviation | All values | Yes | Yes |
Conclusion
Quartile Deviation is a robust and simple measure of dispersion that focuses on the interquartile range, making it especially valuable for skewed datasets and distributions with outliers. Though it lacks mathematical flexibility, it plays a crucial role in descriptive statistics and is highly relevant for UGC NET Commerce exam preparation.