   SEARCH HOME Math Central Quandaries & Queries  Question from cecil, a parent: the average of six number is 84. what is the total Cecil,

To find the average of a collection of numbers you find the total of the numbers, call it T, you count how many numbers there are, call it N and you divide the total by the number of numbers. That is you calculate

average = T/N.

I am going to call the average A so

A = T/N.

So, for example if the total T is 75 and the number of numbers N is 5 then

A = T/N = 75/5 = 15.

For aother example suppose you know that the total is 54 and the average is 18. What is the number of numbers n?

Since I know that

A = T/N

I know that

18 = 54/N

Multiply both sides by N to get

18 × N = 54

so

N = 54/18 = 3.

Now for your problem you know that N = 6 and A = 84. What is T?

I hope this helps,
Penny

Cecil,

The average (A) is the total (T) divided by the number (N) of items.

A = T/N.

If you want to know the total T then we "solve" this equation for T:

T = A * N.

So the total is the average times the number of items.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.