Section 4: Statistics Functions 53
Mean
The ’ function computes the arithmetic mean (average) of the x- and
y-values using the formulas shown in Appendix A and the statistics
accumulated in the relevant registers. When you press | ’ the
contents of the stack lift (two registers if stack lift is enabled, one if not);
the mean of x () is copied into the X-register as the mean of y () is
copied simultaneously into the Y-register. Press ® to view .
Example:
From the corrected statistics data we have already entered
and accumulated, calculate the average fertilizer application, , and
average grain yield, , for the entire range.
Keystrokes Display
| ’
40.00
Average kg of nitrogen, , for all cases.
®
6.40
Average tons of rice, , for all cases.
Standard Deviation
Pressing | S computes the standard deviation of the accumulated
statistics data. The formulas used to compute s
x
, the standard deviation
of the accumulated x-values, and s
y
, the standard deviation of the
accumulated y-values, are given in Appendix A.
This function gives an estimate of the population standard deviation from
the sample data, and is therefore termed the sample standard deviation.
*
When you press | S, the contents of the stack registers are lifted
(twice if stack lift is enabled, once if not); s
x
is placed into the X-register
and s
y
is placed into the Y-register. Press ® to view s
y
.
*
When your data constitutes not just a sample of a population but 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
n
−1n
from the formula used for the S function. The difference between the values is small
for large n, and for most applications can be ignored. But 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 z, the mean () of the data to the data before pressing
|S. The result will be the population standard deviation. (If you subsequently
correct any of your accumulated data values, remember to delete the first mean value
and add the corrected one.)
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