Calculating Average Starting Time
Date: 06/23/2003 at 19:28:43 From: Patti Subject: Calculating the average starting time How do you average a series of starting times to get the average starting time? Let's say the times were 9:30 a.m., 10:15 a.m., 11:45 a.m., 1:30 p.m. and 11:30 a.m. I've tried averaging the times as written; converting times after 12:00 so they don't appear less than, say, 11:00; converting them to a decimal form; combining "easy" times (9:00 + 10:00) to get a partial average and then attempting to average these with the remaining times. Depending on how I combine the times, I get different answers. Do you count the earliest time as a "base" time and calculate the elapsed time of the other starting times from there? Do you include the earliest time when you average the rest? Thank you for your assistance.
Date: 06/23/2003 at 21:36:30 From: Doctor Rick Subject: Re: Calculating the average starting time Hi, Patti. There are many ways you could do this, and if done correctly, they will all give the same answer. You must be doing something wrong, perhaps misunderstanding how to convert minutes and seconds to decimal form, or how to combine partial averages (which may require "weighted averaging"). Here is one way to average the times you have listed: 9:30 a.m. = 9 hr 30 min = 9 + 30/60 = 9.5 hr past midnight 10:15 a.m. = 10 hr 15 min = 10 + 15/60 = 10.25 11:45 a.m. = 11 hr 45 min = 11 + 45/60 = 11.75 1:30 p.m. = 13 hr 30 min = 13 + 30/60 = 13.5 11:30 a.m. = 11 hr 30 min = 11 + 30/60 = 11.5 ----- 56.5 hr 56.5 divided by 5 = 11.3 hr = 11 hr + 0.3*60 min = 11 hr 18 min Here is another way: 9 + 10 + 11 + 13 + 11 = 54 hours; divide by 5 ==> 10.8 hour = 10 hr + 0.8 * 60 min = 10 hr 48 min 30 + 15 + 45 + 30 + 30 = 150 min; divide by 5 ==> 30 min 10 hr 48 min + 30 min = 10 hr 78 min = 10 hr + 1 hr + 18 min = 11 hr 18 min See, I got the same answer both ways. The first time I expressed everything in hours since midnight, averaged, and converted back to hours and minutes. The second time I averaged the hours since midnight and the minutes separately, then added the two averages. Do these two methods show you what you were doing wrong? I'll be glad to discuss it further if you are still unsure of what you're doing. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 06/29/2003 at 15:44:35 From: Patti Subject: Thank you (Calculating the average starting time) Dear Doctor Rick, Thank you very much for your assistance. I'm still not sure what I was doing wrong before, but when I applied your two methods to my other problems I got the same answer both times. I also tried it using fractions of an hour and that worked, too. Thanks again! Patti
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