HP 12C, User Manual

Page: 97 / 288

Section 6: Statistics Functions 97
File name: HP 12c Pt Converted_user's guide_English_HDP0F123E02_080207 Page: 11 of 281
Printed Date: { 2007/8/2Dimension: 14.8 cm x 21 cm
To continue summing data pairs, press
gÖg^
before entering more data.
Note:
In some cases involving data values that differ by a relatively small
amount, the calculator cannot compute the standard deviation or the linear
estimation accurately because such calculations would exceed the precision
of the calculator. For instance, while the standard deviation of the values
1,999,999; 2,000,000 and 2,000,001 is 1; the standard deviation
returned by the hp 12c platinum is 0 due to the effect of roundoff. This will
not happen, however, if you normalize the data by keying only the
difference between each value and the mean or approximate mean of the
values. In the preceding example, the correct result can be obtained using
the values –1, 0 and 1 instead. Just remember to add the difference
(2,000,000) back to the calculation of the average.
Linear Estimation
With two-variable statistical data accumulated in the statistics registers, you can
estimate a new
y-value (
yˆ
) given a new x-value , and estimate a new x-value (
xˆ
)
given a new y-value .
To calculate
yˆ
and
Q
1. Key in a new x-value .
2. Press
gR
.
To calculate
xˆ
:
1. Key in a new y-value .
2. Press
gQ
.
Example: Using the accumulated statistics from the preceding problem, estimate
the amount of sales delivered by a new salesperson working 48 hours per week.
Keystrokes Display
48
gQ 28,818.93
Estimated sales for a 48 hour
workweek.
The reliability of a linear estimate depends upon how closely the data pairs would,
if plotted on a graph, lie in a straight line. The usual measure of this reliability is
the correlation coefficient,
r . This quantity is automatically calculated whenever
yˆ
or
xˆ
is calculated; to display it, press
~
. A correlation coefficient close to 1
or –1 indicates that the data pairs lie very close to a straight line. On the other
hand, a correlation coefficient close to 0 indicates that the data pairs do not lie
closely to a straight line; and a linear estimate using this data would not be very
reliable.