Transcript Frequencies and the normal distribution

Frequencies and the normal
distribution
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Calculate the mean (average) and standard
deviation of the House –fly wing data
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Calculate the sample size (count)
of the data
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Calculate the minimum and maximum
of the data
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Make a range of data starting at the Min plus
0.00001 and going to the Max by 0.1’s
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Warning: Array formula
Array formulas have results
that span several cells
instead of just one.
They require:
1) Highlighting enough cells
for the complete answer
2) Clicking Ctrl-Shift-Enter
instead of just Enter.
If you attempt to edit part
of an array formula result,
problems occur. Use the
Esc key to get out of it.
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Highlight cells D2:D21 (for the answer) and insert the
formula =FREQUENCY(A2:A101,C2:C21) and then hit
Ctrl-Shift-Enter
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A frequency is the number of times something occurs – in
this case the values up to and including 3.6, then the
values between 3.6 (exclusive) and 3.7 (inclusive), etc.
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Make a quick (unformatted, un-designed) XY
Scatter graph
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Normal distribution
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Use Excel’s formula for the
normal distribution
Notice that we have
used absolute
addressing for the
mean B$2 and
standard deviation
B$4. That means
when the formula is
copied elsewhere the
2 and 4 are held
fixed.
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The 4th argument is
whether or not we
want to sum the
distribution
everything from
negative infinity up
to and including a
value – we said no.
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Before comparing we need two more steps. The first is to divide the
frequencies by the sample size turning them effectively into
probabilities
Instead of saying the
value 4.2 occurred 7
times in a sample size
of 100, we say 4.2
occurred 0.07 or 7%
of the time.
Note the count
requires absolute
addressing.
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The normal distribution has to be multiplied
by the Δx – the separation between our
values
We had gone up by 0.2’s
instead of by 0.1’s there
would be roughly half as
many Frequencies with
roughly twice the value
they have now.
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Highlight columns C, F & G (only where
there’s data) and Insert an XY-Scatter chart.
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Apply a Chart Layout (e.g. 1) under Design.
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Change the title and axis labels
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Format the axis to have a Minimum of 3
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Right click on a data point and choose
Select Data
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Select a data set, click Edit and give the
series a name.
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Result – see legend
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Right click on the second (normal dist.) series
and choose Change Series Chart Type. Choose
Smooth Lines.
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Result
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Histogram: highlight columns C & D and choose
Insert Column Chart
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Right click and choose Select Data
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Highlight Series 1 and click Remove
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Highlight Series 2 and click Edit under
Horizontal Axis Labels
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Then highlight the C column and click OK
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Result so far
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Choose a Layout (e.g. 7) and label axes
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Add a title (if you haven’t got one already)
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Right click on the columns and choose Format
Data Series. Choose the gap width to be 0%.
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Choose a Solid Line and a Border Color.
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Result
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