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FBLA Data Science & AI

Probability & Statistics Foundations — Full Lecture

🧩 Why This Section Matters

Probability and statistics are the foundation of data science and AI.

Before AI can learn or make predictions, humans must:

Understand data

Summarize it

Measure uncertainty

Describe patterns

FBLA focuses on conceptual understanding, not heavy math.

1️⃣ Measures of Central Tendency

(How we describe the “center” of data)

🔹 Mean (Average)

Definition

The mean is the sum of all values divided by the number of values.

Key Property

Highly affected by outliers

Example

Test scores: 70, 72, 74, 76, 100

Mean = (70+72+74+76+100)/5 = 78.4

📌 The score of 100 pulls the mean upward.

🔹 Median (Middle Value)

Definition

The median is the middle value when data is ordered.

Why Median Is Important

Resistant to outliers

Best for skewed data (income, housing prices)

Two Rules

Odd number of values → middle number

Even number of values → average the two middle numbers

📌 FBLA often asks which measure is least affected by outliers → Median

🔹 Mode (Most Frequent Value)

Definition

The value that appears most often.

Notes

A dataset can have:

One mode

Multiple modes

No mode

📌 Used more with categorical data.

🔹 Range (Simple Measure of Spread)

Definition

Range = Maximum − Minimum

Key Point

Uses only two values

Very sensitive to outliers

📌 Range describes spread, not center.

2️⃣ Measures of Variability

(How spread out the data is)

🔹 Variance

Definition

The average squared distance from the mean.

Why Square?

Makes all values positive

Penalizes large deviations