GraphingGraphing

Have fun GraphingHave fun Graphing

DataData

Data is information. Look at these Data is information. Look at these examples:examples:

Magic Johnson’s heightMagic Johnson’s height The number in centimeters of snow that fell at The number in centimeters of snow that fell at

Timberline Lodge every day for one monthTimberline Lodge every day for one month The number of Kilometers from New York to The number of Kilometers from New York to

Los AngelesLos Angeles

Scientists use data all of the time. Data helps predict the weather, improve stereo equipment and aid in the fast recovery of patients in the hospital. As scientists, you’ll need to be able to record information, evaluate experiments and draw conclusions. To do this, you will need to know how to use data tables and draw graphs.

Data TablesData Tables

If we collect just a little bit of data it’s no If we collect just a little bit of data it’s no problem to keep track of it. But what problem to keep track of it. But what happens when we get a lot? To organize data happens when we get a lot? To organize data we use a data table. Here is a data table we use a data table. Here is a data table constructed for an imaginary experiment.constructed for an imaginary experiment.

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

Data tables begin with a title. The tile of this data table is “Heating of Compound X”. The title tells the reader exactly what the data in the table refers to. Without a title, it’s possible that the person studying the data table wouldn’t be able to figure out what all of the numbers meant.

Heating of Compound X

Variables and UnitsVariables and Units A data table include variables and units. A A data table include variables and units. A

variable describes what information you are variable describes what information you are recording. A unit tells how you are going to recording. A unit tells how you are going to measure that variable.measure that variable.

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

Heating of Compound X

In this data table, the first row of data is the time variable which is recorded in units of minutes. It is easy to figure out the units because they are always in parenthesis. The second row is for the temperature variable measured in degrees Celsius.

Ordered pairsOrdered pairs Data is organized in a data table. If you look carefully, you’ll find the Data is organized in a data table. If you look carefully, you’ll find the

numbers are organized in groups called ordered pairs. They are numbers are organized in groups called ordered pairs. They are called ordered pairs because the numbers always go together. called ordered pairs because the numbers always go together.

Look at the table again and you’ll see that the combination of 2 Look at the table again and you’ll see that the combination of 2 minutes and 23 degrees Celsius (2 min, 23minutes and 23 degrees Celsius (2 min, 2300C) is one ordered pair.C) is one ordered pair.

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

Heating of Compound X

5 minutes and 45 degrees Celsius (5 min, 450C) is another ordered pair.

There are 11 ordered pairs in this data table.

Now if for some reason Now if for some reason you find a data table you find a data table that runs up and down that runs up and down instead of across, the instead of across, the ordered pairs are still ordered pairs are still there, just side by side there, just side by side now.now.

00 2020

11 2121

2 2 2323

33 2727

44 3535

55 4545

66 6161

77 6969

88 7171

99 7373

1010 7474

Time (min) Temp (0C)

Heating of Compound X

A Complete Data TableA Complete Data Table

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

Heating of Compound X

A properly constructed data table follows these guidelines:

1. A descriptive title

2. Variables describing what information has been collected

3. Units telling how those variables were measured

4. Data collected in ordered pairs

5. All work done neatly

Reading a GraphReading a Graph

A graph is an exact A graph is an exact picture of picture of information in a information in a data table. It’s data table. It’s usually a line that usually a line that shows the shows the relationship relationship between all of the between all of the numbers in a data numbers in a data table. The table. The following data table following data table and graph are for and graph are for the Heating of the Heating of Compound X.Compound X.

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

Heating of Compound X

Heating of Compound X

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Plotting a GraphPlotting a Graph If a graph is an exact picture of the data If a graph is an exact picture of the data

table, then everything that’s in the data table table, then everything that’s in the data table has to be in the graph!has to be in the graph!

1.1. The same descriptive titleThe same descriptive title

2.2. The same variables and unitsThe same variables and units

3.3. The same dataThe same data

The Secret is knowing what to do with the The Secret is knowing what to do with the ordered pairs. Take the second ordered pair ordered pairs. Take the second ordered pair (1 min, 21(1 min, 2100C) and split them up. Place the 1 C) and split them up. Place the 1 minute along the horizontal axis labeled minute along the horizontal axis labeled “Time” at the 1 minute mark. Put the 21“Time” at the 1 minute mark. Put the 2100C C on the vertical axis labeled “Temperature” at on the vertical axis labeled “Temperature” at the 21the 2100C mark. Now follow each line into the C mark. Now follow each line into the middle until they both meet.middle until they both meet.

Intersection of the linesIntersection of the lines The point where these two lines cross The point where these two lines cross

is called the intersection of the lines. is called the intersection of the lines. The point showint the location of the The point showint the location of the intersection is called a data point.intersection is called a data point.

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Intersection for ordered pair (1,21)

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Data point for ordered pair (1,21)

Plotting a GraphPlotting a Graph

To read a graph, find a data point. Simply To read a graph, find a data point. Simply trace the horizontal and vertical lines back trace the horizontal and vertical lines back to each axis and you’ve found the ordered to each axis and you’ve found the ordered pair for the data point.pair for the data point.

Locating the data point by finding the Locating the data point by finding the intersection of the two lines is called intersection of the two lines is called plotting. Once all of the data points are plotting. Once all of the data points are plotted and a line is drawn to connect them plotted and a line is drawn to connect them you have a simple way to “read” all the you have a simple way to “read” all the data in a data table quickly.data in a data table quickly.

Plotting a Line GraphPlotting a Line Graph

If you follow these simple guidelines If you follow these simple guidelines then making a graph is easy. First, then making a graph is easy. First, draw the horizontal and vertical axes draw the horizontal and vertical axes using your ruler. using your ruler.

Vertical Axis

Horizontal Axis

Next, look at the data table and decide Next, look at the data table and decide which variable is most consistent. In our which variable is most consistent. In our example it is time. The most consistent example it is time. The most consistent variable is the variable labeled on the variable is the variable labeled on the horizontal axix. Label the vertical axix with horizontal axix. Label the vertical axix with the other variable.the other variable.

Tem

p (

0C

)

Time (minutes)

Third, number each axis in even intervals. Intervals are determined by looking at the smallest and largest numbers in the data table. Devise an even way to space them along the axis.

Heating of Compound X

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

For time, the smallest number is 0 and the largest is 10. The numbers between are in even intervals of 1’s. Because the work is already done, label the horizontal right off the data table.

1 2 3 4 5 6 7 8 9 10

Tem

p (

0C

)

Time (minutes)

To determine the labels for the vertical axis, we To determine the labels for the vertical axis, we need to think a bit. The smallest number is 20, need to think a bit. The smallest number is 20, the largest number is 74. The rest of the the largest number is 74. The rest of the numbers between are hardly what you would call numbers between are hardly what you would call even. Label the axis by 10’s and then plot the even. Label the axis by 10’s and then plot the data points, we’ll get a good picture of the data. data points, we’ll get a good picture of the data.

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Once the axis are drawn and labeled, it is time Once the axis are drawn and labeled, it is time to plot the data points. Using the data table to plot the data points. Using the data table below, split up the ordered pairs. Find each below, split up the ordered pairs. Find each half of the pair on the respective axis and half of the pair on the respective axis and follow the lines until they intersect. follow the lines until they intersect.

Heating of Compound X

Time (min)Time (min) 00 11 22 33 44 55 66 77 88 99 1010

Temp (Temp (0C) 2020 2121 2323 2727 3535 4545 6161 6969 7171 7373 7474

1101009080706050403020100

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Heating of Compound X

Once all of the data points are plotted, line Once all of the data points are plotted, line up the data points with a ruler and connect up the data points with a ruler and connect the dots. When all the points are connected, the dots. When all the points are connected, you’ll have a line graph like the one below.you’ll have a line graph like the one below.

1101009080706050403020100

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Tem

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Time (minutes)

Heating of Compound X

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Be sure to copy the descriptive title from the top of the data table onto the top of the graph.