Tutoring math, you see topics come in and go out of style.  Arithmetic mean is such a concept….

 
In math, the “mean” is known by some as the average. To find the mean of 65 and 83, add them and divide by two:

mean=(65+83)/2=148/2=74

Between 65 and 83, 74 is an arithmetic mean: it’s in the middle between 65 and 83.

What if you were asked for two arithmetic means between 65 and 83? They would be two numbers that offer a path from 65 to 83 in three equal steps, as shown:

65,mean_1,mean_2,83

The approach is to imagine the distance covered from number to number in the sequence above. Let’s call the distance d:

65,mean_1,mean_2,83=65,65+d,65+2d,65+3d

Therefore

65+3d=83

Subtract 65 from both sides:

3d=18

Divide both sides by 3:

d=6

Therefore, the distance of each “jump” in the sequence

65,mean_1,mean_2,83

is 6. The sequence is

65,71,77,83

The two arithmetic means between 65 and 83 are 71 and 77.

Historically, arithmetic mean is a term often seen on exams; it comes and goes. Now, if you do see it, you’ll more likely be prepared:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.