Associated Topics || Dr. Math Home || Search Dr. Math

### Averaging Minutes and Seconds

```Date: 07/03/2002 at 01:59:09
From: Corey Tharp
Subject: Averaging Minutes and Seconds

I need the average time of 20 different times.  If I punch it in on a
calculator, it is incorrect due to time being on a 60 unit cycle
compared to a 10 unit cycle on the calculator.  I understand this, but
still can't figure out how to get around it.

I read a problem in your archives that was similar, but I still don't
appreciated.
```

```
Date: 07/03/2002 at 14:09:30
From: Doctor Rick
Subject: Re: Averaging Minutes and Seconds

Hi, Corey.

I think you're saying that you punched in, say, 4.25 for 4 minutes
and 25 seconds, and it didn't come out right. The correct way is
first to convert seconds to minutes: for instance, 25 seconds = 25/60
minutes, so 4 minutes, 25 seconds = 4 + 25/60 = 4.41667 minutes.
Convert each time from minutes and seconds to decimal minutes in this
way, then average.

Perhaps we can speed things up. First add up the seconds ONLY, for
all 20 times. Then divide by 60 to convert all the seconds to
minutes. Then continue adding the minutes part of each time. Finally,
divide by the number of times (DON'T count the minutes and seconds
separately) to do the averaging.

Does this make sense to you? Here's why it works. When you average 3
times, you should do this:

(2m,25s + 3m,10s + 5m,50s)/3

We need to express all in minutes so we can add:

(2+25/60 + 3+10/60 + 5+50/60)/3

We can rearrange the terms using the commutative property of addition:

(2 + 3 + 5 + 25/60 + 10/60 + 50/60)/3

We can combine the divisions into a single division using the
distributive property of multiplication by 1/60 (which is what
division by 60 is):

(2 + 3 + 5 + (25 + 10 + 50)/60)/3

That's what I did, only I put the seconds first so we wouldn't need
parentheses with the calculator:

25 + 10 + 50 =     85
/ 60 =              1.41667
+ 2 + 3 + 5 =      11.41667
/ 3 =               3.80556 minutes

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Calendars/Dates/Time

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search