HP 12c Owners Manual

							  Section 5: Additional Operating Features  71 
 
File name: hp 12c_users guide_English_HDPMBF12E44  Page: 71 of 209   
Printered Date: 2005/7/29    Dimension: 14.8 cm x 21 cm 
 
The Display 
Status Indicators 
Six indicators that appear along the bottom of the display signify the status of the 
calculator for certain operations. These status indicators are described elsewhere 
in this handbook where the relevant operation is discussed. 
 
Number Display Formats 
When the calculator is first turned on after coming from the factory or after 
Continuous Memory has been reset, answers are displayed with two decimal 
places. 
Keystrokes Display  
19.8745632\ 
19.87  
5- 
14.87  
Although you see only two decimal places, all calculations in your hp 12c are 
performed with full 10-digit numbers. 
 
When only two decimal places are displayed, numbers are rounded to two 
decimal places: if the third digit is 5 through 9, the second digit is increased by 
one; if the third digit is 0 through 4, the second digit is not affected. Rounding 
occurs regardless of how many decimal places are displayed. 
Several options are provided for controlling how numbers appear in the display. 
But regardless of which display format or how many displayed decimal places you 
specify, the number inside the calculator — which appears altered in the 
display — is not altered unless you use the B
, !
, V
, Ý
, or #
 functions. 
Standard Display Format.
 The number 14.87 now in your calculator is 
currently being displayed in the standard display format with two decimal places 
shown. To display a different number of decimal places, press f 
followed by a 
digit key (0 through 9) specifying the number of decimal places. In the following 
examples, notice how the displayed form of the number inside the calculator — 
14.87456320 — is rounded to the specified number of digits.  
						

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Keystrokes Display   
f4 
14.8746  
f1 
14.9  
f0 
15.  
f9 
14.87456320 Although nine decimal places were 
specified after f
, only eight are 
displayed since the display can 
show a total of only 10 digits. 
The standard display format, plus the specified number of decimal places, remain 
in effect until you change them; they are not reset each time the calculator is turned 
on. However, if Continuous Memory is reset, when the calculator is next turned on 
numbers will be displayed in the standard display format with two decimal places 
shown. 
If a calculated answer is either too small or too large to be displayed in the 
standard display format, the display format automatically switches to scientific 
notation (described below). The display returns to the standard display format for 
all numbers that can be displayed in that format. 
Scientific Notation Display Format 
 
In scientific notation, a number is displayed with its mantissa at the left and a 
two-digit exponent at the right. The mantissa is simply the first seven digits in the 
number, and has a single, nonzero digit to the left of the decimal point. The 
exponent is simply how many decimal places you would move the decimal point in 
the mantissa before writing down the number in standard format. If the exponent is 
negative (that is, there is a minus sign between it and the mantissa), the decimal 
point should be moved to the left; this occurs for any number less than 1. If the 
exponent is positive (that is, there is a blank space between it and the mantissa), 
the decimal point should be moved to the right; this occurs for any number greater 
than or equal to 1. 
To set the display format to scientific notation, press f.
. For example (assuming 
the display still shows 14.87456320
 from the preceding example):  
						

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Keystrokes Display  
f. 
1.487456 01  
The exponent in this example indicates that the decimal point should be moved 
one decimal place to the right, giving the number 14.87456, which is the first 
seven digits of the number previously in the display. 
To set the display back to standard display format, press f
 followed by the 
desired number of decimal places. Scientific notation display format remains in 
effect until you change to the standard display format; it is not reset each time the 
calculator is turned on. However, if Continuous Memory is reset, when the 
calculator is next turned on the standard display format, with two decimal places, 
will be used. 
Mantissa Display Format.
 Because both the standard display format and 
scientific notation display format often show only a few digits of a number, you 
may occasionally want to see all 10 digits — the full mantissa — of the number 
inside the calculator. To do so, press f
CLEARX
 and hold down the X
 key. 
The display will show all 10 digits of the number as long as you hold down the 
X
 key; after you release the key, the number will again be displayed in the 
current display format. For instance, if the display still contains the result from the 
preceding example: 
Keystrokes Display  
fCLEARX 
1487456320 All 10 digits of the number inside 
the calculator. 
 
1.487456 01 Display returns to its former contents 
when the X
 key is released. 
f2 
14.87 Returns display to standard format. 
Special Displays 
Running.
 Certain functions and many programs may take several seconds or 
more to produce an answer. During these calculations, the word running
 flashes 
in the display to let you know that the calculator is running. 
Overflow and Underflow.
 If a calculation results in a number whose 
magnitude is greater than 9.999999999 ×10
99, the calculation is halted and the 
calculator displays 9.999999 99 
(if the number is positive) or –9.999999 99
 
(if the number is negative). 
If a calculation results in a number whose magnitude is less than 10
–99, the 
calculation is not halted, but the value 0 is used for that number in subsequent 
calculations.  
						

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Errors.
 If you attempt an improper operation — such as division by zero — the 
calculator will display the word Error
 followed by a digit (0
 through 9
). To clear 
the Error
 display, press any key. This does not execute that key’s function, but 
does restore the calculator to its condition before the improper operation was 
attempted. Refer to Appendix C for a list of error conditions. 
Pr Error. 
If power to the calculator is interrupted, the calculator will display Pr 
Error
 when next turned on. This indicates that Continuous Memory — which 
contains all data, program, and status information — has been reset. 
The  key 
Suppose you need to subtract $25.83 from $144.25, and you (mistakenly) key in 
25.83, press \
, then key in 144.25. But then you realize that when written 
down on paper, the desired calculation reads 144.25 – 25.83, so that you have 
unfortunately keyed in the second number first. To correct this mistake, merely 
exchange the first and second numbers by pressing ~
, the exchange key. 
Keystrokes Display  
25.83\144.25 
144.25 Oops! You mistakenly keyed in the 
second number first. 
~ 
25.83 Exchanges the first and second 
numbers. The first number keyed in is 
now in the display. 
- 
118.42 The answer is obtained by pressing 
the operation key. 
The ~
 key is also useful for checking the first number entered to make sure you 
keyed it in correctly. Before pressing the operation key, however, you should press 
~
 again to return the second number entered to the display. Regardless of how 
many times you press ~
, the calculator considers the number in the display to 
be the second number entered. 
The  Key 
Occasionally you may want to recall to the display the number that was there 
before an operation was performed. (This is useful for doing arithmetic calculations 
with constants and for recovering from errors in keying in numbers.) To do so, 
press gF
 (last x).  
						

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Arithmetic Calculations With Constants 
Example:
 At Permex Pipes a certain pipe fitting is packaged in quantities of 15, 
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package. 
Keystrokes Display  
15\ 
15.00 Keys first quantity into calculator. 
4.38 
4.38 Keys unit cost into display. 
§ 
65.70 Cost of a package of 15. 
75 
75. Keys second quantity into display. 
gF 
4.38 Recalls unit cost — which was last 
number in display before §
 was 
pressed — into display. 
§ 
328.50 Cost of a package of 75. 
250 
250. Keys third quantity into display. 
gF 
4.38 Recalls unit cost into display again. 
§ 
1,095.00 Cost of a package of 250. 
Another method for doing arithmetic calculations with constants is described on 
page 177. 
Recovering From Errors in Digit Entry 
Example:
 Suppose you want to divide the total annual production for one of your 
firm’s products (429,000) by the number of retail outlets (987) in order to 
calculate the average number distributed by each outlet. Unfortunately, you 
mistakenly key in the number of outlets as 9987 rather than as 987. It’s easy to 
correct: 
Keystrokes Display  
429000\ 
429,000.00  
9987 
9,987. You haven’t noticed your mistake 
yet. 
z 
42.96 About 43 products per outlet — but 
that seems too low! 
gF 
9,987.00 Recalls to the display the number 
that was there before you press z
. 
You see that you keyed it in wrong. 
429000\ 
429,000.00 Begins the problem over. 
987z 
434.65 The correct answer.  
						

							 
76 
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  Section 6 
Statistics Functions 
Accumulating Statistics 
The hp 12c can perform one- or two-variable statistical calculations. The data is 
entered into the calculator using the _
 key, which automatically calculates and 
stores statistics of the data into storage registers R
1, through R6. (These registers are 
therefore referred to as the “statistics registers.”) 
Before beginning to accumulate statistics for a new set of data, you should clear 
the statistics registers by pressing f
clear²
.
* 
In one-variable statistical calculations, to enter each data point — referred to as an 
“x-value” — key the x-value into the display, then press _
. 
In two-variable statistical calculations, to enter each data pair — referred to as the 
“x and y-values”: 
1. Key the y-value into the display. 
2. Press \. 
3. Key the x-value into the display. 
4. Press _. 
Each time you press _
, the calculator does the following: 
z The number in R1 is increased by 1, and the result is copied into the display. 
z The x-value is added to the number in R2. 
z The square of the x-value is added to the number in R3. 
z The y-value is added to the number in R4. 
z The square of the y-value is added to the number in R5. 
z The product of the x and y-values is added to the number in R6. 
                                                 
*  This also clears the stack registers and the display.  
						

							  Section 6: Statistics Functions  77 
 
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The table below shows where the accumulated statistics are stored. 
 
Register Statistic 
R1 (and display) n: number of data pairs accumulated. 
R2 Σx: summation of x-values. 
R3 Σx2: summation of squares of x-values. 
R4 Σy: summation of y-values. 
R5 Σy2 summation of squares of y-values. 
R6 Σxy: summation of products of x-values and y-values. 
Correcting Accumulated Statistics 
If you discover you have entered data incorrectly, the accumulated statistics can 
easily be corrected: 
z  If the incorrect data point or data pair has just been entered and _ has 
been pressed, press gFg^. 
z  If the incorrect data point or data pair is not the most recent one entered, key 
in the incorrect data point or data pair again as if it were new, but press 
g^ instead of _. 
These operations cancel the effect of the incorrect data point or data pair. You can 
then enter the data correctly, using _
, just as if it were new. 
Mean 
Pressing gÖ
 calculates the means (arithmetic averages) of the x-values (x) and 
of the y-values (
y). The mean of the x-values appears in the display after Ö
 is 
pressed; to display the mean of the y-values, press ~
. 
Example:
 A survey of seven salespersons in your company reveals that they work 
the following hours a week and sell the following dollar volumes each month. How 
many hours does the average salesperson work each week?
 How much does the 
average salesperson sell each month?
 
  
						

							78  Section 6: Statistics Functions 
 
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Salesperson Hours/Week Hours/Week
1 32 $17,000 
2 40 $25,000 
3 45 $26,000 
4 40 $20,000 
5 38 $21,000 
6 50 $28,000 
7 35 $15,000 
To find the average workweek and sales of this sample: 
Keystrokes Display  
fCLEAR² 
0.00 Clears statistics registers. 
32\ 
17000_ 
32.00 
1.00  
First entry. 
40\ 
25000_ 
40.00 
2.00  
Second entry. 
45\ 
26000_ 
45.00 
3.00  
Third entry. 
40\ 
20000_ 
40.00 
4.00  
Fourth entry. 
38\ 
21000_ 
38.00 
5.00  
Fifth entry. 
50\ 
28000_ 
50.00 
6.00  
Sixth entry. 
35\ 
15000_ 
35.00 
7.00  
Total number of entries in the 
sample. 
gÖ 
21,714.29 Mean dollar sales per month (x). 
~ 
40.00 Mean workweek in hours (y).  
						

							  Section 6: Statistics Functions  79 
 
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Standard Deviation 
Pressing gv
 calculates the standard deviation of the x-values (sx) 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 sy 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 σx 
~ 
5.58 σy 
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.  
						

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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: 
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  
48gQ 
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. 
Example: 
Check the reliability of the linear estimate in the preceding example by 
displaying the correlation coefficient. 
Keystrokes Display  
~ 
0.90 The correlation coefficient is close to 
1, so the sales calculated in the 
preceding example is a good 
estimate. 
To graph the regression line, calculate the coefficients of the linear equation 
y = A + Bx. 
1. Press 0gR to compute the y-intercept (A). 
2. Press 1gR~d~- to compute the slope of the line (B).