Marshall, What I actually wrote is :
"The standard deviation is a unit of measurement of the range of values of a population or sample set which do not equal the mean. By definition a population or sample set of one does not have a range as it equals the mean." in reply to your statement "one has a standard deviation of 1" The above statement of mine remains true! A sample set of one measurement or a population with one member has no deviation...how can it. you write : > It depends on how you look at it. If I have a radiation counter, and take > one 1 minute sample, and get 100 counts, then I have a sample set of one. > But it DOES have a standard deviation, and the standard deviation is the > square root of the mean, which is 100. Thus the standard deviation is 10, > despite having only one sample. This come right out of statistics. I > personally was project manager for nuclear counting systems for 26 years, > and used these relationships all the time. The example you use is one sample set of one reading, the mean equals the sample (sum of the observations divided by the number observations). The sample sd is NOT the square root of the mean, it is the square root of the sum of the squares of the observations minus the mean divided by the sample size minus one. In your example : the square root of 100 - 100 squared divided by 1-1 equals zero. > You are thinking of the "measured" standard deviation, and I am speaking of > the computed standard deviation. If sufficient number of samples are taken, > then the two will match. Similar computations can be made for flipping > coins. The theoretical basis is sound, so even if you flip a coin a certain > number of times you can predict the mean and standard deviation, even > without doing it. You can only compute the standard deviation if you have a reasonably sized sample or population or know the probability for the outcome of each measurement. When flipping coins the probability of a head or tail is 0.5 (this is known as a binomial distribution) and the sd for this is the Square root of the number of observations times the probability times one minus the probability. The other type of observation you note (counts per unit time) is known as a Poisson distribution. The square root of the average count per unit time (lambda) equals its sd which I guess is where you are coming from, but this only applies in very particular circumstances and needs a large enough population of observations times to establish an average. Ivan. --- Outgoing mail is certified Virus Free. Checked by AVG anti-virus system (http://www.grisoft.com). Version: 6.0.215 / Virus Database: 101 - Release Date: 16/11/2000 -- The silver-list is a moderated forum for discussion of colloidal silver. To join or quit silver-list or silver-digest send an e-mail message to: [email protected] -or- [email protected] with the word subscribe or unsubscribe in the SUBJECT line. To post, address your message to: [email protected] Silver-list archive: http://escribe.com/health/thesilverlist/index.html List maintainer: Mike Devour <[email protected]>
