Data & Probability

Statistics

• Mean: sum of values ÷ number of values
• Weighted mean: if groups have different sizes, weight each mean by its count.
• Outlier effect: one extreme value can pull the mean far from the median. Median is a more robust centre.
• Interquartile range (IQR): Q3 − Q1, measures the middle 50% spread.

Data Displays

• Box plot: shows min, Q1, median, Q3, max.
• Scatter plot: shows relationship between two variables; a trend line (line of best fit) can be added.
• Histogram: like a bar chart but for continuous data; bars touch each other.

Probability

Compound events:

• Independent events (one does not affect the other): P(A and B) = P(A) × P(B)
• Mutually exclusive (can't both happen): P(A or B) = P(A) + P(B)

Example: Roll a die twice. P(both 6) = 1/6 × 1/6 = 1/36.