Hi Frank:\ I flunked statistics in college. It was the hardest course I ever took. So I've often wondered how a math guy like you would analyze the average or mean or standard deviation or Root Mean square or whaterever you call it errors in an EOT graph.
I came up with that 7 minute average a very long time ago. If I remember correctly, I just added up all the EOT values for every week of the year (from an EOT table). The negative values cancelled out the positive values and the sum was 7 minutes. I suppose you could also do it with thinking like this: If at worst, a sundial reading is off by about 16 minutes, And at best, it is off by 0 minutes, Then on average, it is off by 16/2 = 8 minutes It seems to make sense. But I'm probably wrong. Like I said- I flunked statistics! John -----Original Message----- From: Frank King [mailto:[email protected]] Sent: Tuesday, February 15, 2011 5:04 AM To: John Carmichael Cc: 'Frank King'; [email protected]; [email protected] Subject: Re: part 2 of longitude correction Dear John, I looked into your interesting assertion about the Equation of Time. You say: On the average, it is only off [mean time] by about seven minutes... It isn't really appropriate to use the term average here because we are not dealing with random variables or errors. We are just looking at a conversion scheme for going from one time system to another. That didn't stop me taking a look and, essentially, agreeing with your figure! Three pedantic points first: 1. The average of the Equation of Time is, of course, zero. 2. The average absolute value is just over seven minutes and this is your figure. 3. The RMS value [Root Mean Square] is probably more useful and that is about 8.75 minutes which is more than I expected intuitively. Here are some intriguing figures in which the left-hand column shows minutes and the right-hand column show the percentage of the time that the absolute value of the Equation of Time is less than the associated number of minutes: mins %age 1 7.7 2 16.2 3 25.2 4 37.0 5 42.5 6 49.6 7 58.4 8 61.4 9 64.4 10 67.9 11 71.2 12 73.4 13 79.5 14 86.3 15 92.1 16 95.6 17 100.0 For example, is you pick a day of the year at random, there is a 25.2% chance that your local sun time is within 3 minutes of your local mean time. Expressed the other way we have: 10% 1m 13s 25% 2m 58s 50% 6m 02s 75% 11m 58s 90% 14m 14s 95% 15m 52s 100% 16m 26s I was surprised that the 75% figure was so high, close to 12 minutes. Maybe my calculations are wrong! All the best Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
