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In statistics, while measures of central tendency tell us the center of the data, they don’t explain how the data is spread out around that center. That’s where Measures of Dispersion come in. These measures help us understand the variability, consistency, and reliability of data—making them essential for research, data analysis, and UGC NET exams.

What Are Measures of Dispersion?

Dispersion refers to the extent to which values in a dataset differ from the average (mean, median, or mode). In simpler terms, it tells us how spread out the data is.

A low dispersion means data points are close to the average; high dispersion means they are scattered.

Common Measures of Dispersion

Here are the four most commonly used measures:

1️⃣ Range

Formula:

Range=Highest Value−Lowest Value

Example:
For the dataset: 45, 50, 55, 60, 70
Range = 70 – 45 = 25

Simple but very sensitive to outliers.

2️⃣ Quartile Deviation (Interquartile Range)

Formula:

Q.D.=�3−�12

Where:

• �1 = First quartile (25th percentile)
• �3 = Third quartile (75th percentile)

Use:
Best when median is used as the measure of central tendency. Ignores extreme values.

3️⃣ Mean Deviation (Average Deviation)

Formula:

M.D.=∑∣�−�∣�

Where:

• � = Each data point
• � = Mean or median
• � = Number of observations

Use:
Measures the average distance of all data points from the mean/median. Less sensitive to outliers than variance.

4️⃣ Standard Deviation (SD)

Formula:

SD=∑(�−�ˉ)2�

Where:

• �ˉ = Mean
• � = Each data value
• � = Total number of values

Most reliable and widely used measure of dispersion.

Variance

Formula:

Variance=(Standard Deviation)2

Used primarily in further statistical applications like ANOVA, regression, etc.

Why Are Measures of Dispersion Important?

• Help assess risk and volatility (e.g., in stock markets)
• Indicate data consistency and quality
• Used to compare different datasets
• Crucial in educational assessment, quality control, and economic analysis

UGC NET Tip:

Prepare for:

• Direct formula-based numerical questions
• Conceptual MCQs (e.g., “Which measure is least affected by extreme values?”)
• Interpretation-based questions involving SD and variance

Sample MCQ:
Which measure of dispersion is considered most reliable?
A. Range
B. Mean Deviation
C. Standard Deviation
D. Quartile Deviation
Correct Answer: C. Standard Deviation

Conclusion

Measures of Dispersion are as important as measures of central tendency in understanding the complete picture of a dataset. Whether you're evaluating test scores, market performance, or experimental results, dispersion tells you how trustworthy and stable your average value is.

For UGC NET, a clear understanding of both concepts and calculations will give you a competitive edge.

Bonus Tip:
Make a formula cheat sheet for Range, QD, MD, SD, and Variance. Practice with real datasets to build speed and accuracy.

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