My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 14th, 2011, 07:02 AM   #21
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,934
Thanks: 1128

Math Focus: Elementary mathematics and beyond
Re: Arithmetic mean: Why use its computation as its definiti

Quote:
Originally Posted by Envroe
is a single value meant to characterize the entire set of a values collectively.
How does one go about choosing a value for ?
greg1313 is online now  
 
August 14th, 2011, 01:20 PM   #22
Newbie
 
Joined: Aug 2011

Posts: 9
Thanks: 0

Re: Arithmetic mean: Why use its computation as its definiti

Quote:
Originally Posted by CherryPi
Since we're talking about things that have been forgotten by the populous:

The method of squaring, cubing, and 'n'ing--finding roots of equations manually--has been forgotten. I recall there being a method similar to division, but I also recall a common sensical method. So here is my challenge to you: What are those two methods? (Bonus points if applied uniquely and specially to fractional powers!)
Yes, not totally forgotten, but buried away in the dusty halls of yesteryear (along with slide rules, calculating devices such as "Consul" The Educated Monkey), nomographs, etc. Probably better discussed in a new thread. I know that finding the n-th root begins by segmenting the number in groups of n digits, usually with apostrophes, and then the division-like process begins. Then there's Newton's method of approximation.

There's also methods for multiplying (yes, multiplying) on your fingers, and probably lots of other cool math methods. I have my own method of multiplying longhand (especially squaring) that's more efficient and involves much fewer "carries".

Quote:
Originally Posted by greg1313
Quote:
Originally Posted by Envroe
is a single value meant to characterize the entire set of a values collectively.
How does one go about choosing a value for ?
That's what the derivation determines by setting the sum of the residuals to zero.

However, you could calculate it step-wise, beginning with some nominal value (eg, zero seems like a good value to begin for the estimate ). Then, calculating the sum of the residuals, and using the result to determine which way to move the estimate along the number line.
For example, using the set of {4, 5, 9}, the sum of residuals is as follows:

? ?
0 ? 18
1 ? 15
2 ? 12
3 ? 9
4 ? 6
5 ? 3
6 ? 0
7 ? -3
8 ? -6
9 ? -9
etc

The estimate can be adjusted until the sum of the residuals equals zero (and then the mean would equal the value of at that point), or the sum of residuals can be set to zero and the mean determined from it.
Evroe is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
arithmetic, computation, definition



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Computation of an integral. ZardoZ Complex Analysis 0 May 4th, 2013 01:12 PM
computation of pi (?) unm Number Theory 1 November 17th, 2012 09:58 AM
Computation of L(4) mathbalarka Calculus 9 August 31st, 2012 05:40 AM
Precision Arithmetic: A New Floating-Point Arithmetic Chengpu Real Analysis 3 June 2nd, 2010 11:37 AM
Precision Arithmetic: A New Floating-Point Arithmetic Chengpu Linear Algebra 0 May 23rd, 2010 04:55 PM





Copyright © 2019 My Math Forum. All rights reserved.