6/03/2010 @ 9:39 PM
Relations
In this unit, you will mostly learn about scatter plots. Also, you will learn about the line/curve of best fit, linear/non-linear relationships, different trends in data, first differences, distance-time graphs, and the scientific process. 


First, let's look at the scientific process. The process is as follows:
1) Write a hypothesis
2) Perform an experiment
3) Collect data
4) Organize data (spreadsheet, table of values)
5) Display data (scatter plot, graphs)
6) Analyze data (look for trends/relationships)
7) Conclusion- state if your hypothesis was true or not

Basically, all this means is you make a hypothesis, perform an experiment, get all the data, and come to a conclusion with the data you have.


EXAMPLE: Drivers' age VS risk of car accident
As the drivers' age increases, the risk of car accidents increases.
As the drivers' age increases, the risk of car accidents do not increase.

Hours studying VS final grade
As the hours studying decreases, the final grade will decrease.
As the hours studying decreases, the final grade will not decrease.

EXAMPLES OF: Primary Data & Secondary Data
-I go around to all the grade 9 classrooms asking for their favourite colour out of the two- red or blue. (PRIMARY)
-I go on Statistics Canada and search up how many deaths were reported in Canada in 2005. (SECONDARY)

Another thing we learned about was scatter plots. Scatter plots show the relation between two variables.
An example of a scatter plot graph is -HERE-
A scatterplot has the independent variable on the x-axis, and the dependent variable on the y-axis.
For example, the number of classes missed as an impact upon one's final grade. Since the independent variable is the number of classes missed, it is displayed on the x-axis, while the final grade is displayed on the y-axis (because it depends on the number of classes missed).

On a scatterplot, there is usually a line of best fit. It shows a trend or pattern on a scatterplot, and it is used to make predictions.

A few tips when drawing the line of best fit:

  • Line follows Trend
  • Goes through as many points as possible
  • There are an equal number of points above and below the line
  • It can be used to predict.
When a scatterplot has a non-linear relation, it is not possible to use a line of best fit- so instead, we use a curve of best fit. It is basically a curve that has the same properties as the line of best fit- but curved.


Scatter plots have 3 main correlations, and they are:
  • Positive Correlation- increasing to the right
  • Negative Correlation- decreasing down to the right
  • No correlation- no pattern

If you want to be more specific, you can add "strong" or "weak" correlation.

  • Positive Strong Correlation/Strong Positive Correlation- Data strongly increases to the right
  • Positive Weak Correlation/Weak Positive Correlation- Data weakly increases to the right
  • Negative Strong Correlation/Strong Negative Correlation- Data strongly decreases to the right
  • Negative Weak Correlation/Weak Negative Correlation- Data weakly decreases to the right
Of course, no correlation is just left as it is. 

First Differences are the increases/decreases in the y-values in a table. They represent the change in y.
TIP: The x-values must go up by 1- consecutive values.


How to calculate first differences:
-Subtract the y-values from the bottom-up
-Can be from top to bottom, or bottom to top

<---Example


Therefore, the first difference is (-2).
TIP: First differences is also the slope.

Since first differences are used to find if a relation is linear/non-linear,
the example shows that the relation is linear.

If the first differences do not match up/are constant, the relation is non-linear.
TIP: For first differences, a positive first difference means a positive correlation, and a negative first difference means a negative correlation.

As well as that, we learned about distance-time graphs.
The distance you travel depends on how long you've been traveling for.
So, distance is put on the y-axis and time is put on the x-axis.

The equations for distance time graphs are as follows:



























EXAMPLES: 

A snail can move approximately 0.30 meters per minute. How many meters can the snail cover in
15 minutes?
ANSWER: D = speed x time
                  D = 0.30 (15)
                  D = 4.5m 

May drives 150 km in 5 hours. What is her speed?
ANSWER: Speed = d/t
                          S = 150 / 5
                          S = 30km/hr

How long did it take Mayu to run 40km in an average of 4km/h?
ANSWER: T = d/s
                  T = 40/4
                  T = 10 hours

An example of a distance-time graph:


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Hello, my name is Sohyun Kim, and I am in grade 9. This site is for my math summative project, so no hateful comments please. I generally like to read, draw, read manga, and watch anime in my spare time.
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definitions.
Polynomials: Algebraic expressions made up of terms
Monomial: 1 term
Binomial: 2 terms
Trinomial: 3 terms
Terms: Made up of a coefficient and variable(s)
Power: Product of identical factors and consists of 2 parts- exponent and base. Coefficient: ----
Variable: ----
Constant/constant term: A term with no variable
Hypothesis: A theory or statement that is either true or false
Statistics: The collection, organization, and analysis of numerical data
Primary Data: Data that comes from experiments and surveys done by researchers
Secondary Data: Data that already exists- comes from sources such as the internet, magazines, and Statistics Canada
Interpolation: Prediction involving a point within the set of data
Extrapolation: Prediction involving a point outside the set of data
Linear Relation: Relation between 2 variables, forms a straight line
Non-Linear Relation: Relation between 2 variables, does NOT form a straight line
Curve of best fit: Curve that comes closest to the points of a non-linear relation
First Differences: -----
Slope: The steepness of a line- ratio of the rise to the run between both points
Direct Variation: A relationship between 2 variables in which one variable is a constant multiple of the other
Partial Variation: When a relationship between 2 variables have both a fixed and variable amount
Continued -HERE-

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