Range – Calculation & Uses 📏📉

Range is the simplest measure of dispersion. It shows how far the values in a dataset spread from lowest to highest.

Range is useful for quick comparisons, understanding variability, and detecting extreme fluctuations.

Definition

Range is the difference between the highest and lowest values in a dataset.

Formula

Range = Highest Value – Lowest Value

Coefficient of Range (Relative Measure)

Coefficient of Range = (H – L) / (H + L)

Where:

• H = highest value
• L = lowest value

Solved Examples

Example 1 — Simple Range

Heights of 5 students (in cm): 150, 160, 165, 155, 170

Highest = 170
Lowest = 150
Range = 170 – 150 = 20 cm

Example 2 — Coefficient of Range

Using the same data:

Coefficient = (170 – 150) / (170 + 150)
             = 20 / 320
             = 0.0625

A value of 0.0625 indicates relatively low dispersion.

Example 3 — Range in Business

A shop recorded daily sales (₹): 8,000; 9,500; 12,000; 6,000; 10,000

Highest = 12,000
Lowest = 6,000
Range = 6,000

This suggests significant variation in daily sales.

Merits of Range ✔️

• Very easy to calculate
• Quick indicator of variability
• Useful in quality control
• Effective when extreme values matter (temperature, rainfall, stock prices)

Demerits of Range ❌

• Depends only on two values: highest & lowest
• Ignores all middle values
• Highly affected by extreme values
• Not a reliable measure for detailed statistical analysis

Uses of Range in Business & Economics 📌

• Monitoring stock price volatility
• Weather forecasting (temperature variation)
• Quality control in manufacturing
• Sales fluctuations analysis
• Risk identification in finance

Summary ✨

• Range = H – L
• Simplest absolute measure of dispersion
• Coefficient of Range = relative, unit-free version
• Easy but unreliable for detailed analysis

Quiz Time 🎯