# Finding the average

Finding the average or the mean is a very straightforward concept. If you have a set of numbers, the average is found by adding all numbers in the set and dividing their sum by the total number of numbers added in the set.

We can generalize the concept of average with the formula below:

Let x1,x2,x3,......,xn be a set of numbers, average = (x1 + x2 + x3,+......+ xn)/n

Let us illustrate with examples:

Example #1:

Get the average of the following set of numbers:

5,4,12,2,1,6

Step 1:

Find the sum:

Sum = 5+4+12+2+1+6= 30

Step 2:

Divide 30 by 6 (the total number of numbers) 30 divided by 6 is 5, so the average or mean is 5

Example #2:

Get the average of the following set of numbers:

5,10,20,5,10

Find the sum:

Sum = 5+10+20+5+10 = 50

Divide the 50 by 5 (the total number of numbers added) 50 divided by 5 is 10, so 10 is the average or mean.

## Finding the average when the numbers in the set are the same.

When all the numbers in the set are the same, it is easy to find the average.

Example #3

Find the average of the following set of numbers:

6, 6, 6

6 + 6 + 6 = 18

18/3 = 6

Example #4

Find the average of the following set of numbers:

12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 132

132/11 = 12

What can we conclude from example #3 and example #4?

When the numbers in the set are all the same, the average is just the number itself.

## Finding the average when some of the numbers in the set are negative numbers.

Example #5

-5, 2, -1, 8

-5 + 2 + -1 + 8 = 4

4/4 = 1

Example #6

-8, 2, -11, 3, 0, 2

-8 + 2 + -11 + 3 + 0 + 2 = -12

-12/6 = -2

Example #7:

Mr. Peter collected 125 pencils from students during the past 5 days. On the average, how many pencils did he collect each day?

Average = 125/5 = 25

Example #8:

Last week, Samuel ordered pizza every day. After collecting all his receipts and getting the total, he realized that he spent a total of 63 dollars on pizza. On the average, how much money did he spend on pizza each day?

Average = 63/7 = 9

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