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\nIn math, the “mean” is known by some as the average. To find the mean of 65 and 83, add them and divide by two:<\/p>\n
mean=(65+83)\/2=148\/2=74<\/p>\n
Between 65 and 83, 74 is an arithmetic mean: it’s in the middle between 65 and 83.<\/p>\n
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:<\/p>\n
65,mean_1,mean_2,83<\/p>\n
The approach is to imagine the distance covered from number to number in the sequence above. Let’s call the distance d:<\/p>\n
65,mean_1,mean_2,83=65,65+d,65+2d,65+3d<\/p>\n
Therefore<\/p>\n
65+3d=83<\/p>\n
Subtract 65 from both sides:<\/p>\n
3d=18<\/p>\n
Divide both sides by 3:<\/p>\n
d=6<\/p>\n
Therefore, the distance of each “jump” in the sequence<\/p>\n
65,mean_1,mean_2,83<\/p>\n
is 6. The sequence is<\/p>\n
65,71,77,83<\/p>\n
The two arithmetic means between 65 and 83 are 71 and 77.<\/p>\n
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:)<\/p>\n