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Section 6: Statistics Functions 79
File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 79 of 209
Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm
Standard Deviation
Pressing
gv
calculates the standard deviation of the x-values (s
x
) and of the
y-values (s
y
). (The standard deviation of a set of data is a measure of the dispersion
around the mean.) The standard deviation of the x-values appears in the display
after
v
is pressed; to display the standard deviation of the y-values, press
~
.
Example:
To calculate the standard deviations of the x-values and of the y-values
from the preceding example:
Keystrokes Display
gv
4,820.59
Standard deviation of sales.
~
6.03
Standard deviation of hours worked.
The formulas used in the hp 12c 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.
*
Keystrokes Display
gÖ
21,714.29
Mean (dollars)
_
8.00
Number of entries + 1.
gv
4,463.00
σ
x
~
5.58
σ
y
To continue summing data pairs, press
gÖg^
before entering more data.
*
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.