This document defines and provides examples of independent and dependent variables, continuous and discrete data, and correlation. It discusses: - Independent variables are what happens first and affect dependent variables. Dependent variables depend on independent variables and are what happens second. - Continuous data involves measuring something that happens continuously like time, distance, or height. Discrete data involves counting things like people or cars. - Correlation describes the relationship between independent and dependent variables. Positive correlation means both variables increase together. Negative correlation means one decreases as the other increases. No correlation means the variables do not change together.

1. Independent and Dependent
Variables
Continuous and Discrete Data
Correlation

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

3. (The dependent variable is plotted on the Y axis)
Independent Variable
The independent variable is always located on the
_________ of a graph.
The independent variable STANDS ALONE.
The independent variable is what happens _______.
x-axis
FIRST

4. 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.

5. Dependent Variable
The dependent variable is always located on the
_________ of a graph.
It is usually the _______ in a table or equation.
The dependent variable DEPENDS on the
________________.
The dependent variable is what happens _______.
y-axis
“y”
independent variable
2nd

6. The dependent variable
is a function whose value
is determined by the
independent variable.
The dependent variable
is tested.

7. 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

8. 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 sodas
Total money
Amount of time
Number of houses

9. Continuous Data
Data 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

10. Discrete Data
You 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

11. • Independent variable, (GOES ON THE X AXIS)
causes a change in (Dependent Variable, GOES
ON THE Y AXIS) and it isn't possible that
(Dependent Variable) could cause a change in
(Independent Variable).
• For example:
• (Time Spent Studying, X AXIS) causes a change in
(Test Score, Y AXIS) and it isn't possible that (Test
Score) could cause a change in (Time Spent
Studying).
• We see that "Time Spent Studying" must be the
independent variable and "Test Score" must be the
dependent variable because the sentence doesn't
make sense the other way around.

12. Let’s Practice
Look 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.
continuous
continuous
discrete
continuous
discrete

13. Example
Kadence 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 90 100 110 120
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

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

15. Positive Correlation
• As one variable
increases, so
does the other.
y
x

16. Example of positive
correlation…
The longer you exercise, the more
calories you burn.
*As exercise increases, calories burned increases
Can you think of one?

17. Negative Correlation:
• As one variable
increases, the
other
decreases.
y
x

18. 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?

19. No Correlation:
• As one variable
increases, you
cannot tell what
the other is
doing.
y
x

20. 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?

21. 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

22. 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