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Statistics
One of the nicest features of the RPN calculator (besides the fact that it is programmable) is that it can compute statistics such as mean and standard deviation and perform least squares curve fits of experimental data. These operations share a small number of keystrokes.
Let's start by learning about mean and standard deviation. Imagine that you are a teacher and you have just finished grading your students' test papers. You are very fortunate to have a small class size of only 12 students and the 12 test grades were:
The calculator uses certain of its registers
(data memory locations) whenever you ask
it to compute statistics. These are data memory locations 10 through 15
which are known as the Summation registers. Before starting a new
statistical computation you want to clear these registers so that old
data does not pollute the new results. This is the purpose of the ClearSum
key which looks like
(the funny symbol is Sigma, the capital S letter in the Greek alphabet, S for "sum").
You could get the same effect by using the ClearREG
keystroke (
)
which clears all 30 of the registers. We will further discuss the calculator's
registers in the section entitled data memory.
You are now ready to enter the test scores. Type in the first test score and
then hit Sum+ (). The X location of the operand
stack does not show the test score but rather displays the number 1 to remind you
that you have entered 1 data point. Next type in the second test score and
again hit Sum+. The calculator's LED display now shows the number 2. Continue
in this manner (note that you are NOT employing the ENTER key) until you have
entered all 12 test scores and the display shows that you have entered 12
data points.
Since the calculator now has all the data points you can ask it for the
mean and the standard deviation. To ask for the mean use the Mean
keystroke () which causes
the mean of the data points to be placed into the X stack location.
For these 12 test scores the mean score was 84.
To ask for the standard deviation use the StdDev keystroke
(
) which causes
the standard deviation of the data points to be placed into the X stack location.
For these 12 test scores the standard deviation among the scores was 8.41 .
The standard deviation describes how tightly grouped the test scores were.
For most types of data, the vast majority of the data points will be within three
standard deviations of either side of the mean.
If you make a mistake while entering a data point you can use
the CLX key ("clear X") to clear the X stack location. But if you have already hit
the Sum+ keystroke before you realize the error then CLX will not be
sufficient. You can either start over (that is, type ClearSum and then
re-enter all the data points) or else again enter the erroneous data point
and then hit the
Sum- ()
keystroke.
The Sum+, Sum-, Mean, and StdDev keystrokes are actually more powerful than I have let on. Every time you hit the Sum+ keystroke both the number in the X stack location and the number in the Y stack location are added into separate running totals. When you later hit the Mean key the X stack location will show the mean of all the X values you entered and the Y stack location will show the mean of all the Y values you entered. Thus you can really perform two averaging operations simultaneously. This will become useful when we start dealing with Cartesian plots whose data points are (x,y) pairs.
The calculator will give you an error if you try the following keystroke
sequence:
. This is an
error because you have asked for the average of 0 data points, which can't
be computed. Similarly, you can't compute the standard deviation of 0
data points. You can compute the average of 1 data point but did you know
that you can't compute the standard deviation
of 1 data point? Standard deviation is only defined when you have 2 or
more data points.
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