02.07.04 |【04】| Use of “Standard Deviation (σ)”
Standard Deviation — SD — σ — sigma.
Measure of Volatility — σ — measure of how dispersed the data to the mean outcome.
Comparison — actual outcomes [V.S] expected value (i.e. mean outcome) — determine how far on average the outcomes deviate from the mean.
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
Low SD — data are clustered around the mean — less volatile — lower risk.
High SD — data are more spread out from the mean — more volatile — higher risk.
Observe the patterns between lower SD and higher SD in the following diagram ▼
Q : What if have 2 probability distributions with different EVs where their SDs not directly comparable?
Solution — Coefficient of Variation — CoV — alternative measure — relative size of the risk.
What is Coefficient of Variation❓
Coefficient of Variation — CoV — ratio of SD (σ) to mean (μ) — measure relative size of the risk.
CoV — show extent of variability in relation to the mean of the population.
Useful — where and when 2 SDs (σ) not directly comparable.
ℹ Using formula.
ℹ Formula ▼
