Statistics for finance · level 1
z-scores
Every normal question becomes easy once the value is expressed in sigmas. Subtract the mean, divide by σ, and read the answer off the 68/95/99.7 ladder.
Worked example: x = 118, μ = 100, σ = 12. z-score?
gap18
σ12
z1.5
Step by step
- 1
Distance from the mean
118 − 100 = 18
- 2
In units of σ
18 / 12 = 1.5
- 3
Say it out loud
1.5 standard deviations above the mean.
x = 118, μ = 100, σ = 12. z-score? = 1.5
The theory behind it
Intuition
A z-score converts any number into 'how many standard deviations from normal', which is what makes outliers comparable across metrics.
Common pitfalls
- ×Using the sample standard deviation where the standard error belongs.
- ×Applying normal-tail intuition to obviously skewed data.
In the interview
Outlier detection in an exhibit: which store is genuinely abnormal.