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Independent and Dependent Variables
Continuous and Discrete DataCorrelation
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In an Algebraic situation, equation, table, or graph, the variables (usually x and y) can be classified as either __________ or _________.
independent
dependent
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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
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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.
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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
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The variable in a function whose value is determined by the independent variable.
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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
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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
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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
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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
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• Graphs of each situation
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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
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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
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Correlation
•It is the relationship that exists between two variables (Independent and dependent).
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Positive Correlation
• As one variable increases, so does the other.
y
x
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Example of positive correlation…
The longer you exercise, the more calories you burn.
*As exercise increases, calories burned increases
Can you think of one?
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Negative Correlation:
• As one variable increases, the other decreases.
y
x
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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?
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No Correlation:
• As one variable increases, you cannot tell what the other is doing.
y
x
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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?
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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
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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