Probability and Statistics

Probability and Statistics

The study of chance data and data analysis

Probability

The likelihood that an event will occur

Probability Formula

Number of desired outcomes over total possible outcomes

Ways to Express Probability

Fractions ratios percents or decimals

Independent Events

Events where one outcome does not affect another

Probability of Independent Events

Multiply the probability of each event

Coin Flip Probability

One half chance of heads on one flip

Two Coin Flips Both Heads

One fourth probability

Die Roll Probability

One out of six chance for a specific number

Two Die Rolls Same Outcome

Multiply individual probabilities

Even Number on a Die

Three out of six possible outcomes

Two Even Rolls Probability

Multiply three sixths by three sixths

Complementary Events

Events where multiple outcomes lead to the desired result

Rolling Two Dice Total Outcomes

Thirty six total outcomes

Probability of Rolling a Two

One out of thirty six

Probability of Rolling a Seven

One out of six

Multiple Ways Outcome

Add probabilities of all successful outcomes

Spinner Probability

Number of successful outcomes over total sections

Comparing Spinner Probabilities

Compare even and odd outcome probabilities

Combinations

Arrangements where order does not matter

Independent Choices

Choices that do not affect one another

Combination Rule

Multiply the number of choices in each group

Combination Example Outfit Choices

Count total possible outfits

Combination Lock Problem

Multiply choices for each dial

Permutations

Arrangements where order matters

Dependent Choices

Choices that affect future options

Permutation Rule

Multiply decreasing whole numbers

Permutation Example Horse Race

Factorial of number of horses

Factorial

A product of whole numbers decreasing to one

Collecting Data

Gathering information through observation or surveys

Survey

A sample used to estimate a population

Good Survey Sample

Random and representative sample

Bias

Results caused by unrepresentative sampling

Skewed Data

Data influenced by limited or unfair sampling

Pie Chart

Shows how parts make up a whole

Bar Graph

Compares quantities or categories

Line Graph

Shows change over time

Table

Organizes numerical data for comparison

Frequency Table

Displays how often values occur

Univariate Data

Data with one variable

Bivariate Data

Data with two variables

Scatter Plot

Graph showing relationship between two variables

Linear Association

Relationship that follows a straight line pattern

Goodness of Fit

How well a model matches data

Measures of Central Tendency

Values that describe the center of a data set

Mean

Average of a data set

Finding the Mean

Add values and divide by number of values

Median

Middle value of an ordered data set

Median with Even Data

Average of two middle values

Mode

Most frequently occurring value

Choosing Mean

Best when data is evenly distributed

Choosing Median

Best when data has outliers

Choosing Mode

Best for trends or popularity