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96 Section 6: Statistics Functions
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 96 of 275
Printed Date: 2005/8/1 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
gv
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 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.
*
Keystrokes Display
gÖ
21,714.29
Mean (dollars)
_
8.00
Number of entries + 1.
gv
4,463.00
σ
x
~
5.58
σ
y
*
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 257, that s will be the population standard deviation,
σ, of the original set.