Statistics and Probability

Mean, median, and mode

Mean $=\frac{\text{sum of values}}{\text{number of values}}$. Median is the middle value once data is ordered (average the two middle values if there's an even count). Mode is the most frequent value.

Grouped data

For grouped/frequency data, use the midpoint of each class interval as a representative value: mean $=\frac{\sum fx}{\sum f}$, where $f$ is frequency and $x$ is the class midpoint.

Range and spread

Range $=$ highest value $-$ lowest value -- the simplest measure of spread.

Basic probability

$P(E)=\frac{\text{number of favourable outcomes}}{\text{total possible outcomes}}$. Probability is always between 0 (impossible) and 1 (certain).

Combined events

• Mutually exclusive (can't both happen): $P(A\text{ or }B)=P(A)+P(B)$.
• Independent (one doesn't affect the other): $P(A\text{ and }B)=P(A)\times P(B)$.