   SEARCH HOME Math Central Quandaries & Queries  Question from Jason:

I have 300 used cars built from 1970 to 1980, I would like to know the average
age by total volume. If I provide the qty built per year, can I determine the average age of the lot (300) by total volume?

 Total built Year built 50 56 30 10 30 25 64 9 12 14 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980

Thanks Hi Jason,

To find the average age of the cars you find the age of each car, total the ages and divided the resulting sum by 300. Since you have the data nicely compiled in a table the calculation is easier than that.

Since this is 2011, to find the age of a car you subtract the year it was built from 2011. Thus for the cars built in 1971 their age is $2011 - 1971 = 40.$ You have 50 cars of this age so adding 40 years, 50 times gives $40 \times 50 = 2000$ years.

Likewise for the cars built in 1972 the sum of their ages is $39 \times 56$ years.

Continuing across the table the sum of the ages of all the cars is

$(40 \times 50) + (39 \times 56) + (38 \times 30) + \cdot \cdot \cdot + (31 \times 40) \mbox{ years. }$

Divide this sum by the number of cars, 300, to obtain the average age of the cars in years.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.