Midterms Algebra Terms Study

Standard Form of a linear equation

A linear equation written in the form Ax + By = C, where A, B, and C are integers.

X-intercept

The value of x when y = 0 in a linear equation.

Y-intercept

The value of y when x = 0 in a linear equation.

Slope-Intercept Form

A linear equation written in the form y = mx + b, where m is the slope and b is the y-intercept.

Point-Slope Form

A linear equation written in the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Correlation Coefficient

A value that indicates the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

Line of Best Fit

A straight line that best represents the data on a scatter plot.

Direct Variation

A relationship between two variables where one is a constant multiple of the other, expressed as y = kx.

Linear Regression

A statistical method used to model the relationship between a dependent variable and one or more independent variables.

Causation

A relationship where a change in one variable directly causes a change in another variable.

Interpolation

Estimating a value within the range of two known values in a data set.

Extrapolation

Estimating a value outside the range of known values in a data set.

Data Alignment

The arrangement of data points to reflect a certain trend or relationship in a scatter plot.

Dependent Variable

The variable that is measured or affected in an experiment, typically represented on the y-axis.

Independent Variable

The variable that is manipulated or controlled in an experiment, typically represented on the x-axis.

Function

A relation where each input has exactly one output.

Linear Function

A function whose graph is a straight line.

Slope

The steepness or incline of a line, calculated as rise over run.

Proportional Reasoning

Using the relationship between quantities to solve problems involving ratios, rates, and proportions.

Conversion Factor

A ratio that expresses how many of one unit are equivalent to another unit.

Unit Rate

A comparison of two measurements in which the second quantity is one unit.

Dimension Analysis

A method for converting units using conversion factors.

Ratio

A comparison of two quantities by division.

Marginal Frequency

The total of the frequency of a certain category in a two-way table.

Joint Frequency

The frequency count for a specific combination of categories in a two-way table.

Conditional Frequency

The frequency of a category given that another event occurred.

Relative Frequency Graphs

Graphs that display the frequency of outcomes relative to the total number of events.

Scatter Plot

A graph that shows the relationship between two variables using points to represent data.

Bar Graphs

A graph that represents categorical data with rectangular bars.

Dot Plots

A simple display of data using dots to represent values.

Two-Way Table

A table that displays data for two categorical variables.

Mean

The average of a set of numbers, calculated by dividing the sum of the values by the number of values.

Median

The middle value of a set of numbers when they are arranged in order.

Mode

The value that appears most frequently in a data set.

Range

The difference between the maximum and minimum values in a set of data.

Outlier

A value that is significantly higher or lower than the other values in a data set.

Statistical Significance

A measure of whether observed data is likely to be due to chance or if it reflects a real effect.

Continuous Variable

A variable that can take on an infinite number of values within a given range.

Discrete Variable

A variable that can take on a countable number of values.

Experiment

A procedure carried out to support, refute, or validate a hypothesis.

Sample

A subset of individuals selected from a larger population.

Population

The entire group that you want to draw conclusions about.

Survey

A method of gathering information from individuals.

Probability

The measure of the likelihood that an event will occur.

Random Sample

A sample that fairly represents a population because each member has an equal chance of inclusion.

Bias

A tendency to favor one outcome over another in data collection.

Statistical Analysis

The process of collecting and analyzing data to identify patterns or relationships.

Histogram

A graphical representation of the distribution of numerical data.

Box Plot

A standardized way of displaying the distribution of data based on a five-number summary.

Five-Number Summary

A summary that provides information about a dataset including minimum, first quartile, median, third quartile, and maximum.

Quartiles

Values that divide a data set into four equal parts.

Interquartile Range (IQR)

A measure of variability, calculated as the difference between the first and third quartiles.

Normal Distribution

A probability distribution that is symmetric about the mean.

Skewed Distribution

A distribution in which values cluster to one side of the mean.

Confidence Interval

A range of values used to estimate the true value of a population parameter.

Hypothesis Testing

A method of making statistical decisions using experimental data.

P-value

The probability level used to determine significance in a hypothesis test.

Null Hypothesis

The hypothesis that there is no effect or difference.

Alternative Hypothesis

The hypothesis that there is an effect or difference.

Type I Error

Rejecting the null hypothesis when it is actually true.

Type II Error

Failing to reject the null hypothesis when it is actually false.

Correlation

A statistical measure that describes the size and direction of a relationship between two variables.

Regression Analysis

A statistical process for estimating the relationships among variables.

Trend Line

A line that best represents the data on a scatter plot.

Outlier Removal

The process of identifying and excluding outliers from a data set.

Trial

A single attempt to measure something in an experiment.

Event

An outcome or a set of outcomes in a probability experiment.

Cumulative Frequency

A running total of frequencies up to the current point in a dataset.

Frequency Distribution

A summary of how often each value occurs in a dataset.

Bimodal Distribution

A distribution with two different modes or peaks.

Multimodal Distribution

A distribution with multiple modes or peaks.

Saturation Point

The point at which a substance can no longer dissolve in a solvent.

Linear Relationship

A relationship that creates a straight line when graphed.

Rate of Change

A ratio that describes how one quantity changes in relation to another.

Standard Deviation

A measure of the amount of variation or dispersion in a set of values.

1) An equation is in the form y = mx + b. What does the coefficient in the equation represent? What does the constant in the equation represent?

The coefficient 'm' represents the slope of the line, indicating how steep the line is and the rate of change of the dependent variable with respect to the independent variable.

Fill in the blank: The ______ is a straight line that best represents the data on a scatter plot.

Line of Best Fit

Fill in the blank: The ______ is a measure of how steep a line is, calculated as rise over run.

Slope.

What is the standard deviation in statistics?

A measure of the amount of variation or dispersion in a set of values.

What is the Standard Form of a linear equation?

A linear equation written in the form Ax + By = C, where A, B, and C are integers.

Fill in the blank: The ______ is a measure of how one quantity changes in relation to another.

Rate of Change

Fill in the blank: The ______ is a relationship that creates a straight line when graphed.

Linear Relationship

Fill in the blank: The ______ is the total of the frequency of a certain category in a two-way table.

Marginal Frequency

What is Regular Format in data representation?

Regular format refers to a structured way of organizing data that follows specific guidelines or conventions for consistency and clarity.