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How to draw a graph

How would you draw a graph of distance as it varies over time using the following data?

Time
in seconds
Distance
in meters
0 0
1 4.9
2 19.6
3 44.1
4 78.4
5 122.5
6 150.1
7 240.1
8 313.6

Using graph paper

Print out some blank graph paper by clicking here.

Hold the page so that the long edge is at the top (landscape orientation). You will see that it has 9 bold lines running vertically and 7 running horizontally. We have to match that to the two columns worth of data in the table above.

Deciding on the orientation and scale

The point of this is to get your graph to fit the page so that it is not squashed up against one side, or too small. It's a question of seeing how to fit the data to the size of the page.

If you look at the data, you'll see that you have 9 rows in the table representing the seconds from 0 to 8. This looks like it would match nicely with the 9 bold lines that run vertically across the page.

Also, we want the time to be on the x axis of the graph, because the chart is going to show how distance varies with time.

The distance in meters has values from 0 to 313.6, and we have to put these on the vertical axis of the graph. 6 x 60 = 360, so perhaps we should represent 60 meters for every horizontal bold line.

Drawing the axis and labeling

We draw a solid pencil line along the bottom bold gray line, and one the left most vertical gray line. Your graph now looks like this.

Along the top of the graph paper, we will write Distance versus Time.

Starting with the bottom axis, which will be for time, we mark 0,1,2 .. 8 every bold line, and on the vertical axis, we mark 0,60,120, 180 .. 360 for the distance in meters.

We also need to label the axis, so we write Time in seconds along the bottom and Distance in meters on the left side.

Your graph now looks like this

Plotting the data

The data start at 0 seconds and 0 meters. So draw an X where the two axis intersect, at 0 seconds and 0 meters.

Next you're going to draw the 4.9 meter point at 1 second. To do this we need to convert 4.9 meters onto the scale where one bold horizontal line equals 60 meters. That bold line occurs every 10 faint lines. So one small block represents 6 meters, and so 4.9 meters is about 80% of the way up a small block. So draw an X on the one second line just short of a small block up.

The third X will be drawn on the 2 second line at 19.6 meters. Converting from meters to blocks: 19.6 ÷ 6 = 3.3 small blocks. Similarly, the three second distance is at 44.1 meters, or 44.1 6 = 7.4 small blocks up.

We do this for all the data..

Time
in seconds
Distance
in meters
Converted to
small blocks
0 0 0
1 4.9 0.8
2 19.6 3.3
3 44.1 7.4
4 78.4 13.1
5 122.5 20.0
6 150.1 25.0
7 240.1 40.0
8 313.6 52.3

Your chart now looks like this

Drawing the curve

We then have to try and draw a line that best fits the points plotted on the chart. Notice that the distance at 6 seconds looks too low for the curve that would run through the other points. We will consider this an anomaly, probably due to experimental error. So we draw a circle around this point and by pass it when you draw the line through all the points as best as you can make it fit. Your chart now looks like this.

Using Microsoft Excel

(The advanced and less recommended method)

How does the computer know that there is an anomaly in the data? It's just going to mechanically draw the curve and include any anomalies. So you need to realize that you cannot just let the computer do what it likes with the data, which is why you really need to understand the manual method first.

In the following example, I draw the graph, and as I go, I notice the anomaly and have to hide the anomalous data in order to get a smooth curve.

The first thing is to enter the data into the spreadsheet:

Select all the data:

Then, tell it to insert a chart:

Select scatter (X-Y):

But now, in the preview, we notice the anomaly at six seconds that bends the curve:

So we have to hide the data at 6 seconds. Close the chart insertion feature and right click on the row corresponding to 6 seconds and select "Hide":

That fixes the problem, so we have to retrace our steps by inserting the graph again as above before continue where we left off..

Label the axis:

Voila!

You can resize it to fit on a full page.