02.07.04 |【04】| Use of “Standard Deviation (σ)”

What is Standard Deviation❓

ℹ Standard Deviation — SD — σ — sigma.


ℹ Measure of Volatility — σ — measure of how dispersed the data to the mean outcome.


ℹ Comparison — actual outcomes [V.S] expected value (i.e. mean outcome) — determine how far on average the outcomes deviate from the mean.

How to measure SD (σ)❓

ℹ Using formula.


ℹ Formula ▼

where :


σ = standard deviation (s.d.)


∑ = sum of


Χ = each value in the data set


X̅ = mean of all values in the data set


n = number of value in the data set

How to interpret SD (σ)❓

ℹ Low SD — data are clustered around the mean — less volatile — lower risk.


ℹ High SD — data are more spread out from the mean — more volatile — higher risk.


ℹ Observe the patterns between lower SD and higher SD in the following diagram ▼

What if…❓

ℹ Q : What if have 2 probability distributions with different EVs where their SDs not directly comparable?


ℹ Solution — Coefficient of Variation — CoV — alternative measure — relative size of the risk.

What is Coefficient of Variation❓

ℹ Coefficient of Variation — CoV — ratio of SD (σ) to mean (μ) — measure relative size of the risk.


ℹ CoV — show extent of variability in relation to the mean of the population.


ℹ Useful — where and when 2 SDs (σ) not directly comparable.

How to measure CoV❓

ℹ Using formula.


ℹ Formula ▼


where :


σ = population standard deviation


μ = population mean

How to interpret CoV❓

ℹ Lower CoV — lesser dispersion — risk lower.


ℹ Higher CoV — greater dispersion — risk higher.


ℹ If — CoV of 0.5 — SD is half size of the mean — where μ > σ.


ℹ If — CoV of 1 — SD = mean — where σ = μ.


ℹ If — CoV of 1.5 — SD is 1.5 times > mean — where σ > μ.


ℹ Audio briefing ▼