Independent and Dependent Variables

Continuous and Discrete DataCorrelation

In an Algebraic situation, equation, table, or graph, the variables (usually x and y) can be classified as either __________ or _________.

independent

dependent

Independent VariableThe independent variable is always located on the

_________ of a graph.

The independent variable is the ________________.

It is usually the ________ in a table or equation.

The independent variable STANDS ALONE (___________).

The independent variable is what happens _______.

x-axis

Input (domain)

“x”

Does not depend

FIRST

The variable in a function whose value is subject to choice is the independent variable. The independent variable affects the value of the dependent variable.

Dependent Variable

The dependent variable is always located on the _________ of a graph.

The dependent variable is the ______________.

It is usually the _______ in a table or equation.

The dependent variable DEPENDS on the ________________.

The dependent variable is what happens _______.

y-axis

Output (Range)

“y”

independent variable

2nd

The variable in a function whose value is determined by the independent variable.

Let’s Practice!

1. A student’s grade depends on how much she studies.

Independent variable:__________Dependent variable:___________2. The height of a plant and the

amount you water it.Independent variable: ___________Dependent variable: _____________

Time studying

grade

Amount watered

height

3. The amount of money you make and the number of hours you work.

Independent variable: _____________

Dependent variable:_____________

4. The number of sodas you buy and the total money spent.

Independent variable:______________

Dependent variable:_______________

5. The number of houses you can paint depends on how much time you have.Independent variable:______________Dependent variable:_______________

Hours worked

Amount of money

Number of sodasTotal money

Amount of timeNumber of houses

Continuous DataData that is continuous is data that _________ happens. You can usually tell that your data is continuous if you are _________ something (i.e. time, distance, length, height, etc.). If your data is continuous, then you will _________ the points on your graph.

continuously

measuring

connect

Discrete DataYou can tell that your data is discrete if you are ________________________ (i.e. number of people, cars, or stories of a building). If your data is discrete, then you will _____________ the points on your graph.

counting or measuring in whole numbers

NOT connect

• Graphs of each situation

Let’s PracticeLook at the situations given in examples 1-5. Decide if the situation would best be classified as either discrete or continuous data.

1. A student’s grade depends on how much she studies.

2. The height of a plant and the amount you water it.

3. The amount of money you make and the number of hours you work.

4. The number of sodas you buy and the total money spent.

5. The number of houses you can paint depends on how much time you have.

continuouscontinuous

discrete

continuous

discrete

ExampleKadence collected data on the number of push-ups she could do in 2 minutes. The table below shows her data.

Time (seconds) 0 10 20 30 40 50 60 70 80 90 10011

0120

Total # Push-ups 0 4 7 9 12 17 20 22 24 27 30 31 35

a. What is the independent variable?

b. Is the data continuous or discrete?

Time (seconds)

Discrete – counting push-ups

Correlation

•It is the relationship that exists between two variables (Independent and dependent).

Positive Correlation

• As one variable increases, so does the other.

y

x

Example of positive correlation…

The longer you exercise, the more calories you burn.

*As exercise increases, calories burned increases

Can you think of one?

Negative Correlation:

• As one variable increases, the other decreases.

y

x

Example of negative correlation…

The longer the air conditioner is turned on, the colder the temperature.

*As time increases, the temperature decreases

Can you think of one?

No Correlation:

• As one variable increases, you cannot tell what the other is doing.

y

x

Example of no correlation…

The number of students in the classroom and the average height.

*As the number of students increases, you cannot tell what the average height will do.

Can you think of one?

Everything…The amount of time you spend in an airplane and the distance between your departure and your destination.

1. What are the independent and dependent variables?

2. Would this situation represent a discrete or continuous situation?

3. What type of correlation is represented in this situation?

Independent: Distance Dependent: Time

Continuous

Negative correlation

Everything again…The number of times you dip a wick into hot wax and the diameter of a handmade candle

1. What are the independent and dependent variables?

2. Would this situation represent a discrete or continuous situation?

3. What type of correlation is represented in this situation?

Independent: The number of dips Dependent: diameter of candle

Discrete

Positive correlation