Math CentralQuandaries & Queries


Question from cecil, a parent:

the average of six number is 84. what is the total


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


N = 54/18 = 3.

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

I hope this helps,



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.

Stephen La Rocque.

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