Averaging Ages

Date: 11/17/1999 at 11:41:06
From: Caroline Reynolds
Subject: Averages

What is the average age of these 4 children?

     John  - 11 yrs. 10 mos.
     Ann   - 12 yrs. 3 mos.
     Sally - 10 3/4 yrs.
     Jim   - 10 1/2 yrs.

Date: 11/17/1999 at 12:58:22
From: Doctor Rick
Subject: Re: Averages

Hi, Caroline,

I don't know what method you have learned to average ages, if you've 
learned one at all, but I can show you a trick I would use.

I'd want first of all to get the years into a single unit. You could 
convert years and months to decimal years, but

     11 yrs. 10 mo. = 11 10/12 yrs. = 11.8333 yrs.

is pretty ugly. You could convert years and months to months, but

     11 yrs. 10 mo. = 11x12+10 mos. = 142 mos.

is a bigger number than I'd like.

Instead, I will just convert the ages to months *after age 10*. For 
instance, John is 1 yr. 10 mo. older than 10, which is 12+10 = 22 mos. 
(You don't have to use 10 years; I just chose that because it's less 
than all the ages, so I don't have to deal with negative numbers.)

If you do this, you will get 4 numbers of months. You average them by 
adding them up and dividing by 4. Then you must convert this number of 
months to years and months, and add the 10 years back onto the answer.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/