📊 Measures of Dispersion
Why just Mean is not enough?
Knowing only the average (mean) return is not enough. We must also understand how values are spread around that average. This spread is called dispersion.
Example: Two stocks may have the same average return, but one may have wild ups and downs (more risk), while the other stays stable. This is where dispersion helps!
Types of Dispersion Measures:
- 📏 Range
- 📐 Mean Absolute Deviation (MAD)
- 📊 Variance
- 📉 Standard Deviation
1️⃣ Range
Formula: Highest Value − Lowest Value
Meaning: It tells us how far the values stretch.
Example: If returns are 5%, 10%, and 25%, then Range = 25% − 5% = 20%
Note: Range is very basic and sensitive to outliers.
2️⃣ Mean Absolute Deviation (MAD)
Definition: The average of the distances (ignoring + or − sign) of each value from the mean.
Formula:
MAD = (Σ |x − x̄|) ÷ n
Why use it? It avoids negative values, so we just see how spread out the values are, not in which direction.
3️⃣ Variance
Definition: The average of squared differences from the mean.
Formula:
Variance = (Σ (x − x̄)²) ÷ n
Note: Not in original units because we square the values.
4️⃣ Standard Deviation
Definition: The square root of variance. It tells us how much the values differ from the average in the original unit.
Formula:
Standard Deviation = √(Σ (x − x̄)² ÷ n)
Note: This is a commonly used risk measure in finance.
🎯 Dispersion tells us the risk hidden behind the average!