Averages

Averages

The average, also known as the arithmetic mean, is found by adding all the numbers in a data set and dividing that number by the total number of data points in the set. On a test, you may be asked to compare the mean and median of a data set and how they are affected by the values of the data points. You may also be asked how changing a single data point in the set affects the mean or how to calculate the mean from a table or graph.

TIPS for solving: 

The most important tip is to always write out the average equation first. It might seem silly, but trust me. Then you just have to plug in the values using x and solve for x.

Example #1:

Answer: J

To find the average between the seven numbers, we add the seven numbers, then divide by 7. We are given six of the seven numbers and the average of all seven. This, we can call the unknown 7th number x and set up our equation:

(82 + 93 + 68 + 93 + 70 + 98 + x) / 7 = 85.

Let’s solve for x:

Multiply both sides by 7:

(82 + 93 + 68 + 93 + 70 + 98 + x) = 595

Combine like terms:

504 + x = 595

Subtract both sides by 504:

x = 91

Links: 

(5 min) How to solve some of the more difficult average questions: 

(12 min) More average word problems: 

(16 min) A deep dive into the average ACT average question: