Statistics and Probability

Statistics

The discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Probability

A measure of the likelihood that an event will occur.

Mean

The average of a set of numbers, calculated by summing all numbers and dividing by the count.

Median

The middle value in a dataset that has been ordered from least to greatest.

Mode

The value that appears most often in a set of data.

Sample Space

The set of all possible outcomes of a random experiment.

Event

A subset of the sample space; a specific outcome or set of outcomes.

Standard Deviation

A measure of the amount of variation or dispersion of a set of values from their mean.

Mean

Sum of all observations divided by the number of observations.

$\bar{x} = \frac{\sum_i=1^{n} x_i}{n}$

Median

The value separating the higher half from the lower half of a data sample.

For odd n, middle term of sorted data; For even n, average of two middle terms.

Mode

Can be one, more than one, or none.

The value that appears most frequently in a data set.

Range

The simplest measure of dispersion.

Maximum Value - Minimum Value

Variance (Sample)

Average of squared differences from the Mean.

$s² = \frac{\sum_i=1^{n}(x_i - \bar{x})²}{n-1}$

Standard Deviation (Sample)

Square root of the variance, measures spread.

$s = \sqrt{s²}$

Probability of an Event

Applies to equally likely outcomes.

$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Probability of A or B

General formula for union of events.

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Probability of A and B (Independent)

For independent events.

$P(A \cap B) = P(A) \× P(B)$

Conditional Probability

Probability of A given that B has occurred.

$P(A|B) = \frac{P(A \cap B)}{P(B)}$