Welcome to the NavList Message Boards.

NavList:

A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

Compose Your Message

Message:αβγ
Message:abc
Add Images & Files
    or...
       
    Reply
    Re: Lunars using Bennett
    From: Frank Reed
    Date: 2008 Apr 06, 20:21 -0400

    Peter, you wrote:
    "The next column shows the difference, and at the bottom of that column
    the standard deviation is displayed: 0.7.  Excel file attached.
    
    If I've understood correctly, the standard deviation should
    approximate 1.22 (0.5xsqrt6)."
    
    Your result, 0.7, is just right. It's not 1.22, because the "step size" for
    this random walk is not constant. In a textbook random walk, you would have
    N steps of equal size A. Then the expected distance after N steps is
    A*sqrt(N). In the case of adding up numbers rounded to the nearest whole
    number, the step size is 0.5 at most, but it's not constant and, on average,
    it's smaller. In fact, what we need is the standard deviation of a uniform
    distribution one unit wide ("uniform" since the fractional difference can
    fall anywhere in the range from -0.5 to +0.5 with equal probability) and
    that happens to be 0.288. And 0.288*sqrt(N) with N=6 is 0.7 just as you
    found. It works. Now in a navigation problem things are rarely this simple,
    so you couldn't directly apply this result, but the general principle is the
    same.
    
     -FER
    
    
    --~--~---------~--~----~------------~-------~--~----~
    Navigation List archive: www.fer3.com/arc
    To post, email NavList@fer3.com
    To unsubscribe, email NavList-unsubscribe@fer3.com
    -~----------~----~----~----~------~----~------~--~---
    
    

       
    Reply
    Browse Files

    Drop Files

    NavList

    What is NavList?

    Join NavList

    Name:
    (please, no nicknames or handles)
    Email:
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.
    Email:

    Email Settings

    Posting Code:

    Custom Index

    Subject:
    Author:
    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site