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HP HP-12c Manual

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Section 6: Statistics Functions 79
Example: To calculate the standard deviations of the x-values and of the
y-values from the preceding example:
The formulas used in the HP 12C Platinum for calculating s
x
, and s
y
give best
estimates of the population standard deviation based on a sample of the
population. Thus, current statistical convention calls them sample standard
deviations. So we have assumed that the seven salespersons are a sample of the
population of all salespersons, and our formulas derive best estimates of the
population from the sample.
What if the seven salespersons constituted the whole population of salespersons.
Then we wouldn’t need to estimate the population standard deviation. We can
find the true population standard deviation (σ) when the data set equals the total
population, using the following keystrokes.
21
To continue summing data pairs, press gÖg^ before entering more data.
Linear Estimation
With two-variable statistical data accumulated in the statistics registers, you can
estimate a new y-value ( ) given a new x-value, and estimate a new x-value ( )
given a new y-value.
To calculate :
1. Key in a new x-value.
2. Press gR.
To calculate :
1. Key in a new y-value.
2. Press gQ.
Keystrokes Display
gv
4,820.59
Standard deviation of sales.
~
6.03
Standard deviation of hours worked.
Keystrokes Display
gÖ
21,714.29
Mean (dollars)
_
8.00
Number of entries + 1.
gv
4,463.00
σ
x
~
5.58
σ
y
21.
It turns out that if you sum the mean of the population into the set itself and find the new s,
computed using the formulas on page 192, that s will be the population standard deviation, σ,
of the original set.
y
ˆ
x
ˆ
y
ˆ
x
ˆ
… 79 …


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