Introduction
Measures of dispersion describe the spread or variability of a data set. While measures of central tendency (mean, median, and mode) give us the average or middle point, measures of dispersion show how much the data values deviate from that central point. Understanding dispersion is essential in social science and development research to interpret the consistency, reliability, and patterns in collected data.
Why Are Measures of Dispersion Important?
- They show how spread out or clustered the data is.
- Help to understand the reliability of averages.
- Enable comparison between different data sets.
- Help identify outliers and anomalies.
Common Measures of Dispersion
1. Range
It is the simplest measure of dispersion and is calculated as the difference between the highest and lowest values in a data set.
Formula: Range = Maximum Value – Minimum Value
Example: If the marks obtained by students are: 40, 50, 60, 70, 80 → Range = 80 – 40 = 40
Limitation: It is affected by extreme values (outliers) and doesn’t reflect the distribution of values between the extremes.
2. Interquartile Range (IQR)
IQR measures the range within which the middle 50% of values fall. It is the difference between the third quartile (Q3) and the first quartile (Q1).
Formula: IQR = Q3 – Q1
Example: In a data set: 10, 15, 20, 25, 30, 35, 40 → Q1 = 15, Q3 = 35 → IQR = 35 – 15 = 20
Benefit: Less affected by outliers, more accurate in skewed distributions.
3. Mean Deviation (Average Deviation)
It is the average of the absolute differences between each value and the mean of the dataset.
Formula: Mean Deviation = Σ|x – Mean| / n
Example: If mean = 50 and values are 40, 50, 60 → Deviation = |40–50| + |50–50| + |60–50| = 10 + 0 + 10 = 20 → Mean deviation = 20/3 ≈ 6.67
4. Variance
Variance measures the average squared deviation from the mean. It gives more weight to extreme values due to squaring.
Formula: Variance (σ²) = Σ(x – mean)² / n
Example: For values 10, 20, 30 with mean = 20:
- (10–20)² = 100
- (20–20)² = 0
- (30–20)² = 100
- Total = 200, Variance = 200 / 3 ≈ 66.67
Limitation: Difficult to interpret as it is in squared units.
5. Standard Deviation
It is the square root of variance and represents the average amount by which values differ from the mean. It is the most commonly used measure of dispersion.
Formula: SD = √Variance
Example: If variance = 66.67 → SD ≈ √66.67 ≈ 8.16
Interpretation: A low SD means data points are close to the mean, while a high SD indicates wide variation.
Use of Measures of Dispersion in Real Life
- Education: To assess variation in student marks.
- Healthcare: To compare blood pressure variations among patients.
- Economics: Income inequality is often measured using dispersion measures.
- Development Studies: Standard deviation is used to compare development indicators between regions.
Conclusion
Measures of dispersion are vital tools in understanding data beyond just averages. They reveal patterns of inequality, variability, and consistency. For accurate and meaningful analysis in development research, both central tendency and dispersion measures must be considered together. Among all, standard deviation is the most versatile and widely used measure in quantitative research.