# average of times

• Jan 12th 2011, 04:05 PM
epsilon8425
average of times
Hi, I need to find the average of the times below (displayed as a time e.g. 8:15 meaning 8 hours 15 minutes not a decimal e.g. 8.25) I know the formula to find the average of a number is:

Mean = sum of elements / number of elements

The times I need to find the average for are:

9:30
8:45
8:30
8:15
8:00
8:00 Because there are 12 pieces of data the mean should lie between this number (8:00)
7:45 and this number (7:45). I think this is a rule but I could be wrong.
7:30
7:00
6:30
6:00
6:00

90.25 / 12 = 7.520833333

I tried the formula above and got 7.52083333 does this answer mean that the average time is 7 hours and 52 minutes? Any help is appreciated. If I have missed anything or my question is unclear let me know and ill do my best to clarify.
• Jan 12th 2011, 04:08 PM
dwsmith
Quote:

Originally Posted by epsilon8425
Hi, I need to find the average of the times below (displayed as a time e.g. 8:15 meaning 8 hours 15 minutes not a decimal e.g. 8.25) I know the formula to find the average of a number is:

Mean = sum of elements / number of elements

The times I need to find the average for are:

9:30
8:45
8:30
8:15
8:00
8:00 Because there are 12 pieces of data the mean should lie between this number (8:00)
7:45 and this number (7:45). I think this is a rule but I could be wrong.
7:30
7:00
6:30
6:00
6:00

90.25 / 12 = 7.520833333

I tried the formula above and got 7.52083333 does this answer mean that the average time is 7 hours and 52 minutes? Any help is appreciated. If I have missed anything or my question is unclear let me know and ill do my best to clarify.

You calculator adds in base 10. The clock minutes base is 60. You need to convert the minutes. For instance, 9:30 would be 9.5.
• Jan 12th 2011, 04:41 PM
epsilon8425
could you please show me how to convert 7.52083333 so it is in hours and minutes? thank you for your quick response.
• Jan 12th 2011, 04:48 PM
dwsmith
You have 4 30, 1 15, and 2 45 minute times

That is 3 hours and 45 minutes.

$\displaystyle \displaystyle\frac{45}{60}=\frac{x}{100}\Rightarro w x=75$

$\displaystyle \displaystyle\frac{3+9+8*5+7*3+6*3+.75}{12}=7.6458 33$

$\displaystyle \displaystyle\frac{64.583333}{100}=\frac{x}{60}$
• Jan 12th 2011, 05:19 PM
epsilon8425
I think I see what you are doing, so by converting the minutes into their decimal equivalents ( 15 minutes as 0.25) you can then add all of the times together and divide by 12 to get the average as a decimal (7.64583333) and then you can convert 0.64583333 into minutes add 7 (for the hours) and the answer is the average, is that right?

I found a calculator online to convert decimal hours into a time and I got 7 hours and 38 minutes 45 seconds (7:39 rounded) is this the average of the times? Thanks for your help so far.
• Jan 12th 2011, 05:21 PM
dwsmith
Correct.
• Jan 12th 2011, 05:40 PM
epsilon8425
Thank you so much for all of your help.
• Jan 12th 2011, 05:46 PM
dwsmith
No problem.
• Jan 13th 2011, 04:21 PM
epsilon8425
Sorry I forgot to ask this yesterday, the answer (7:39) doesn't sit between 8:00 and 7:45 like I thought it was going to, did I get that rule wrong? I just want to make sure 7 hours 39 minutes is the correct average of the times listed in the first post.
• Jan 13th 2011, 04:24 PM
dwsmith
Quote:

Originally Posted by epsilon8425
Sorry I forgot to ask this yesterday, the answer (7:39) doesn't sit between 8:00 and 7:45 like I thought it was going to, did I get that rule wrong? I just want to make sure 7 hours 39 minutes is the correct average of the times listed in the first post.

The number in the middle of a list of data sorted lowest to highest is the median not mean. They are unrelated.
• Jan 14th 2011, 12:27 AM
epsilon8425
thanks again for all of your help it is appreciated.
• Jan 14th 2011, 12:57 PM
HallsofIvy
Quote:

Originally Posted by epsilon8425
could you please show me how to convert 7.52083333 so it is in hours and minutes? thank you for your quick response.

First that means 7 hours and .52083333 of an hour. One hour is 60 minutes so that is 7 houjrs and .52083333 of 60 minutes. "of" here means "multiply" (1/2 "of" 60, for example, is (1/2)(60)= 30 minutes) so .52083333 of 60= (.52083333*60)= 31.2499998. 7.52083333 hours is 7 hours and 31.2499998 minutes. If you want to go further, 0.2499998 of a minute is 0.2499998 of 60 seconds: (.2499998)(60)= 14.999988 seconds so you could reasonably say that "7.52083333 hours" is "7 hours, 31 minutes, and 15 seconds".
• Jan 14th 2011, 01:00 PM
dwsmith
Quote:

Originally Posted by HallsofIvy
First that means 7 hours and .52083333 of an hour. One hour is 60 minutes so that is 7 houjrs and .52083333 of 60 minutes. "of" here means "multiply" (1/2 "of" 60, for example, is (1/2)(60)= 30 minutes) so .52083333 of 60= (.52083333*60)= 31.2499998. 7.52083333 hours is 7 hours and 31.2499998 minutes. If you want to go further, 0.2499998 of a minute is 0.2499998 of 60 seconds: (.2499998)(60)= 14.999988 seconds so you could reasonably say that "7.52083333 hours" is "7 hours, 31 minutes, and 15 seconds".

Halls,

it was added up original within base ten without converting the minutes so the .52083333 part was wrong.