HP 15c Collector's Edition User Manual

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  −1n
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.)

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.