Math 108X Unit 3: Ch 10, Ch 11, Ch 12, C

BYU-I Math 108X Math for the Real World Textbook; Ch 10 Making Predictions from data;

Data analysis

the method of collecting, graphing, and analyzing data in order to understand patterns in the data

Names for input variable

x-variable

independent variable

explanatory variable

predictor variable

Names for output variable

y-variable

dependent variable

response variable

outcome variable

result variable

trendline

the graph of a function that describes the pattern or trend in data represented by input and output variablesc

A correlation between two variables does not?

imply there is a casual relationship

system of equations

a list of two or more equations that use the same input and output variables.

intersection point

satisfies both equations in a system so it represents the solution we are looking for

Independent system

Formed when two lines intersect at one point.

The point where the lines intersect is the solution to the system.

Inconsistent system

is formed when two lines are parallel and never intersect.

has no solution.

dependent system

formed when the two equations in the system actually represent the same line.

Every point on the line is a solution to the system. So the solution has infinitely-many solutions.

What is one way to solve a system of equations

The substitution method

substitution method

to solve a system of equations with this you eliminate one variable from one of the equations by substituting an expression for that variable from the other equation.

Probability

a measurement between 0 and 1 of how likely an event is to happen. An event with a probability of 0 will never happen. An event with a probability of 1 is certain to happen.

sample space

a list of all the possible outcomes of an event

probability model

consists of the sample space along with the probability of each possible outcome.

empirical probability

determined by historical data or by trying the event many times and computing how often the desired outcome occurs

In order for an empirical probability to be accurate,

it must be based on a very large number of trials

theoretical probability

determined by using your knowledge of the situation and mathematical formulas to predict how often the desired outcome will occur in the future

parameter

a number based on a survey of the entire population

statistic

a number based on a survey of just a sample of the population

Statistics are used to estimate …

the true percentage (the parameter) for the whole population.

margin of error

helps us measure how far our statistic might be from the true percentage (the parameter).

=1/√n

n represents the total number of people in the sample

confidence interval

a tool for estimating a parameter. is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence usually 95%

Confidence interval equation

Confidence interval=the statistic+-margin of error

C=x/n+-1/√n

x represents the number of people in the sample with the characteristic

n represents the total number of people in the sample