Year 1 · Foundations · Portfolio & Risk
Statistics & Probability
Build the quantitative language used throughout finance: descriptive statistics, distributions, z-scores, probability, conditional probability, Bayes, sampling and dependence between variables.
LEARNING OBJECTIVES
What you should be able to explain after this lesson
01
Calculate and interpret mean, median, percentiles, variance and standard deviation.
02
Understand distributions, skewness, outliers and why averages can be misleading.
03
Calculate and interpret z-scores and use them to standardize observations.
04
Apply basic probability rules, conditional probability and Bayes' theorem.
05
Explain sampling, standard error and why larger samples usually reduce sampling uncertainty.
06
Distinguish covariance, correlation and causation.
CONCEPT MAPFrom raw data to a financial conclusion
Mean and median summarize different notions of a typical value
CORE FACTS · SAME IN EVERY MODE
The arithmetic mean is the sum of observations divided by the number of observations.
The median is the middle observation after sorting the data, or the average of the two middle observations for an even sample size.
The mean is sensitive to extreme observations; the median is more robust to outliers.
In skewed financial data, mean and median can tell very different stories.
BeginnerTeaching style changes, knowledge does not.
Suppose five returns are 2%, 3%, 4%, 5% and 26%. The mean is 8%, but four of the five observations are below 8%. The median is 4%, which better describes the center of this skewed sample.
FORMULAArithmetic mean
Mean = Σxᵢ ÷ nAdd all observations and divide by the number of observations.
Worked example
(2 + 3 + 4 + 5 + 26) ÷ 5 = 8.
COMPARISON
Mean vs median
| Statistic | Strength | Weakness |
|---|---|---|
| Mean | Uses all observations | Sensitive to outliers |
| Median | Robust to extremes | Uses less magnitude information |
PROFESSIONAL VOCABULARYOutlier / valeur aberrante / outlier Skewness / asymétrie / skewness
An observation unusually far from the rest of the data.
A measure or description of asymmetry in a distribution.