44 Section 3: Numeric Functions
HP-10C to compute s
x
, the standard deviation of the accumulated x-values, and
s
v
, the standard deviation of the accumulated y-values are:
)1(
)(
)1(
)(
2222
−
Σ−Σ
=
−
Σ−Σ
=
nn
yyn
s
nn
xxn
s
yx
These formulas give the best estimates of the population standard deviations
from the sample data. Consequently, the standard deviation given by these
formulas is termed by convention the sample standard deviation. When you
press ´S:
1. The contents of the stack registers are lifted as they are when you press
´’, as described on page 43.
2. The standard deviation of the x-values (s
x
) is calculated using the data
accumulated in registers R
2
(∑x
2
), R
1
(∑x), and R
0
(n) according to the
formula shown above. The resultant value for s
x
is placed in the X-
register.
3. The standard deviation of the y-values (s
y
) is calculated using the
statistical data accumulated in registers R
4
(∑y
2
), R
3
(∑y), and R
0
(n)
according to the formula shown above. The resultant value for s
y
is
available in the Y-register.
Example: Calculate the standard deviation for the corrected coal production
and for the electrical output accumulations used in the preceding examples.
Keystrokes Display
´S
0.429
Standard deviation of
electrical output (X-
register inputs) for the
five-year period.
®
0.080
Standard deviation of
coal production (Y-
register inputs) for the
five-year period.
Retain the preceding statistics in your HP-10C for use in the next example.
When your data constitute not just a sample of a population but rather all of the
population, the standard deviation of the data is the true population standard
deviation (denoted σ). The formula for the true population standard deviation
differs by a factor of
nn )1( −
from the formula used for the S function. For
large n, the difference between the values is small, and for most applications
can be ignored. Nevertheless, if you want to calculate the exact value of the
population standard deviation for an entire population, you can easily do so:
simply add, using the z key, the mean (
x
) of the data to the data and press
´S. The result will be the true population standard deviation of the
original data.
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