Data Analysis & Chance: ACT Statistics Comprehensive Review

Arithmetic Mean

The sum of data values divided by the count of values.

Median

The middle number when data is ordered from least to greatest.

Mode

The value that appears most frequently in a dataset.

Weighted Average

Calculated by multiplying each value by its weight, summing them, and dividing by the total weight.

Range

The difference between the maximum and minimum values in a dataset.

Standard Deviation

A measure of how much values deviate from the mean; higher values indicate more spread.

Outlier

A data point significantly higher or lower than the rest of the data.

Random Sampling

A method where every member of the population has an equal chance of being selected.

Population

The entire group you want to know about, such as all high school students in the US.

Sample

A subset of the population that you actually survey.

Positive Correlation

As one variable increases, the other variable tends to increase.

Negative Correlation

As one variable increases, the other variable tends to decrease.

No Correlation

No predictable pattern exists between the two variables.

Correlation Coefficient (r)

A measurement indicating the strength and direction of a correlation, ranging from -1 to 1.

Linear Regression

A method to predict the value of one variable based on another variable via a linear equation.

Slope (m)

The predicted change in the dependent variable for every one unit increase in the independent variable.

Y-intercept (b)

The predicted value of the dependent variable when the independent variable is zero.

Basic Probability Formula

P(E) = Number of Favorable Outcomes / Total Number of Possible Outcomes.

Independent Events

Events where the outcome of one does not affect the outcome of the other.

Mutually Exclusive Events

Events that cannot occur at the same time.

Empirical Rule

In a normal distribution, 68% of data falls within 1 SD, 95% within 2 SDs, and 99.7% within 3 SDs.

Normal Distribution

A symmetric distribution where the mean, median, and mode are all equal.

Double Counting in Probability

Mistake made when adding probabilities for 'OR' events without subtracting overlapping probabilities.

Geometric Probability

Probability based on the size of a region in relation to the total area.

Bivariate Data

Data that involves two different variables.

Bias in Surveys

Systematic errors that favor certain outcomes in data collection.

Sample Space

The total number of possible outcomes in a probability event.

Quadratic Transformation

A relationship modeled as a quadratic function, typically represented as y = ax^2 + bx + c.