Let's zoom in on one corner of the coordinate plane Let's zoom in on one corner of the coordinate plane. (This corner is called the first quadrant.) The point where the two axes cross has a special name: it is called the origin. The blue lines will help us find points. When you make your own graphs, you can use the lines on your graph paper to help you. (0,0)

Finding Points in the Plane We can find every point in the plane using two numbers. These numbers are called coordinates. We write a point's coordinates inside parentheses, separated by a comma, like this: (5, 6). Sometimes coordinates written this way are called an ordered pair. The first number in an ordered pair is called the x-coordinate. The x-coordinate tells us how far the point is along the x-axis. The second number is called the y-coordinate. The y-coordinate tells us how far the point is along the y-axis.

Estimating Points Sometimes, the point you want to graph is in between points that are marked on the axes. When this happens, you must estimate where to put your point. For example, graph (5, 13) using these axes: (5,13)

Some Rules for All Graphs All of your graphs should have… A title At the top of the graph and underlined It should represent what you are graphing (use your variables)

Some Rules for All Graphs con’t Labeled Axis Use a straight-edge to draw all lines Use the blue lines that are provided for you on the graph paper. Axes should be drawn a few lines in and up from the edge of the paper You must state what is represented on the x-axis and what is represented on the y-axis; include units when necessary

Some Rules for All Graphs con’t The appropriate scale We need the graph to fill up the most paper. To find the right scale, we divide the range of the values by the number of tick marks on that axis. (Range is the highest value – the lowest value). Then we round to a number that is easy to count by.

How to Graph Hold the graph paper the tall way. Title it using the variables. Label the axes; don’t forget to include units. Draw axes a couple of lines up and over Count the number of lines going across the x-axis starting at the zero mark 20 lines Distance vs. Time Distance (m) Time (min)

Scale the x-axis Time (min) Distance (m) 1 2 3 4 5 6 7 8 9 10 Find your range for the x-axis (in science it’s the highest data point because we always start from zero) Time: 10-0=10 so range is 10 Divide the range of the x-axis by the # of lines on the x-axis: 10/20=0.5 0.5 is an easy-to-count by number so count EVERY blue line as 0.5

Scale the x-axis: Distance vs. Time Distance (m) 0 1 2 3 4 5 6 7 8 9 10 Time (min)

Scale the y-axis Repeat for the y-axis: tic marks = 30 lines Time (min) Distance (m) 1 10 2 40 3 35 4 50 5 65 6 70 7 90 8 85 9 100 110 Scale the y-axis Repeat for the y-axis: tic marks = 30 lines Range = 110/30=3.6667 so round to 5; Count the y-axis by 5s Could also count by 4s

Nice Counting Numbers Once in a while you might have to Whole Numbers: 1 2 5 10 15 20 25 50 100 Etc. Decimals: 0.1 0.2 0.25 0.5 Once in a while you might have to count by a different not so nice number!

Make Ordered Pairs (0,0) (1,10) (2,40) Plot data (3,35) (4,50) (5,65) Distance vs. Time (0,0) (1,10) (2,40) (3,35) (4,50) (5,65) (6,70) (7,90) (8,85) (9,100) (10,110) Plot data 140130120110 100 90 80 70 60 50 40 30 20 10 Distance (m) Relationship: The average distanced traveled is fairly constant for each time period. 0 1 2 3 4 5 6 7 8 9 10 Time (min)

Review: All Graphs need: A title At the top and underlined Labeled Axes Axes scaled appropriately (every tick mark increases by the same amount; each axes can be scaled differently)

Some Graphs need: A Key (when necessary) If you are putting more than one line on a graph, it must have a key to distinguish the difference

Different Types of Graphs Tables, charts and graphs are convenient ways to clearly show your data.

There are three basic graph forms. Line Graph Bar Graph Circle (or Pie) Graph Notice on the next few slides how each of the following examples are used to illustrate the data. Choose the best graph form to express your results.

Bar Graph A bar graph is used to show relationships between groups. The two items being compared do not need to affect each other. It's a fast way to show big differences. Notice how easy it is to read a bar graph.

Circle Graph or Pie Graph A circle graph is used to show how a part of something relates to the whole. This kind of graph is needed to show percentages effectively.

Line Graph A line graph is used to show continuing data; how one thing is affected by another. It's clear to see how things are going by the rises and falls a line graph shows.

The same data displayed in 3 different types of graphs. Bar Graph Line Graph Circle (Pie) Graph

Choosing the Right Graph Use a bar graph if you are not looking for trends (or patterns) over time; and the items (or categories) are not parts of a whole. Use a pie chart if you need to compare different parts of a whole, there is no time involved and there are not too many items (or categories). Use a line graph if you need to see how a quantity has changed over time.  Line graphs enable us to find trends (or patterns) over time.

More Examples of Different Graphs

Circle Graph Used to show how the parts relate to the whole

Bar Graph A bar graph contains horizontal or vertical bars. A good way to compare data that can be grouped into a category. The bars do not touch.

Histograms Special type of bar graph Compares different intervals of data rather than categories The ranges used for the intervals must be the same size Bars should touch

Line Graphs Drawn dot-to-dot Shows trends To compare trends between two or more things, you plot different lines for each and include a key

Scatter Plot A scatter plot is a graph made by plotting ordered pairs in a coordinate plane to show the correlation between two sets of data. y-variable x-variable

How do you determine the best-fit line through data points? y-variable Try to get an even number of data points on the line and on each side of the ruler x-variable

Positive Correlation A scatter plot describes a positive trend if, as one set of values increases, the other set tends to increase. 

Negative Correlation A scatter plot describes a negative trend if, as one set of values increases, the other set tends to decrease.

No Trend A scatter plot shows no trend if the ordered pairs show no correlation