Download Using Excel to Graph Data

Using Excel to Graph
Data
Featuring – Mean, Standard
Deviation, Standard Error and
Error Bars.
Physics and Graphs
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So you thought graphs were only
important in mathematics.
In fact they are very important in
physics as they provide the ‘picture’ of
data that you collect while doing an
experiment.
Remember ‘a picture is worth a
thousand words’
Mean Stuff
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The knowledge that any individual measurement
you make in a lab will lack perfect precision often
leads a researcher to choose to take multiple
measurements at some independent variable level.
Though no one of these measurements are likely to
be more precise than any other, this group of
values, it is hoped, will cluster about the true value
you are trying to measure.
This distribution of data values is often represented
by showing a single data point, representing the
mean value of the data, and error bars to represent
the overall distribution of the data.
Exercise – Acceleration of
a Jet Fighter
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Let's take, for example, the time taken for a
jet aircraft to reach and pass through Mach 1.
In this case, the velocity is the independent
variable being manipulated by the researcher
and the time taken is the dependent variable
being recorded.
The velocity is determined by an on board
computer.
Because there is not perfect precision in
recording time with stop watches, 3
trials are carried out and averaged.
Mean Stuff
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The mean, or average, of a group of values
describes a middle point, or central
tendency, about which data points vary.
Without going into detail, the mean is a way
of summarizing a group of data and stating
a best guess at what the true value of the
dependent variable value is for that
independent variable level.
In this example, it would be a best guess at
what the time taken would be for a given
velocity was.
Using Excel to calculate
the mean.
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The mean can be calculated for each time
by using the AVERAGE function in Excel.
You use this function by typing =AVERAGE
in the formula bar and then putting the
range of cells containing the data you want
the mean of within parentheses after the
function name, like this:
Error Bars – Standard
Deviation
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Can you ever know the true values for
time in this example?
No, but you can include additional
information to indicate how closely the
means are likely to reflect the true
values.
You can do this with error bars.
Error Bars – Standard
Error
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There are two common ways you can statistically
describe uncertainty in your measurements.
One is with the standard deviation of a single
measurement (often just called the standard
deviation) and the other is with the standard
deviation of the mean, often called the standard
error.
Since what we are representing the means in our
graph, the standard error is the appropriate
measurement to use to calculate the error bars.
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We can calculate error bars using the data
we have placed in our Excel spreadsheet.
While we were able to use a function to
directly calculate the mean, the standard
error calculation is a little more round about.
First you have to calculate the standard
deviation with the STDEV function.
It is used much the same way AVERAGE
was:
Calculating - Standard
Error
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The standard error is calculated by dividing the
standard deviation by the square root of number of
measurements that make up the mean (often
represented by N).
In this case, 8 measurements were made (N = 8)
so the standard deviation is divided by the square
root of 8.
By dividing the standard deviation by the square
root of N, the standard error grows smaller as the
number of measurements (N) grows larger.
This reflects the greater confidence you have in
your mean value as you make more measurements.
You can make use of the of the square root
function, SQRT, in calculating this value:
Correcting Values for
Significant Figures
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Our original values only had 4
significant figures where the values for
mean, standard deviation and
standard error have less and often
many more.
We need to correct this and again you
can do this within Excel using the
‘Formate Cells’ option
Construction your graph
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Now that we have the appropriate
data we need it’s time to construct an
Excel graph.
First highlight the ‘velocity’ and ‘mean
time’ columns and click on the ‘chart’
value on the tool bar.
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Note that in the constructed graph the
x and y axes are around the wrong
way.
Let’s correct this before continuing!
Click on
‘Series’ in chart
wizard
Reverse the letter
values for the X and Y
axis in these boxes. In
this case A replaced E
and E replaced A
Now the graph has
been correctly
oriented and appears
to have a new shape.
Fill in the ‘Chart Title’
and ‘X and Y axis’
boxes with their
appropriate labels
Error Bars
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With the standard error calculated for
each temperature, error bars can now
be created for each mean.
First click the line in the graph so it is
highlighted.
Now select Format>Selected Data
Series
Click on graph
line –dialogue
box will then
appear
Click ‘Custom’
then highlight
‘Standard
Error’ values
These values will be
the same for +ve
and -ve values
around each point
Press OK
when you
have finished
Look at these
error bars.
Fantastic!
Finished Product –
looking good!