Average Word Problems

There are three main types of average problems commonly encountered in school algebra: Average (Arithmetic Mean), Weighted Average and Average Speed.

Average (Arithmetic Mean)

The average (arithmetic mean) uses the formula:

The formula can also be written as

Example :

The average (arithmetic mean) of a list of 6 numbers is 20. If we remove one of the numbers, the average of the remaining numbers is 15. What is the number that was removed?

Solution:

Step 1: The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e.

sum of original 6 numbers – sum of remaining 5 numbers

Step 2: Using the formula

sum of original 6 numbers = 20 × 6 = 120
sum of remaining 5 numbers = 15 × 5 = 75

Step 3: Using the formula from step 1

Number removed = sum of original 6 numbers – sum of remaining 5 numbers

120 – 75 = 45

Answer: The number removed is 45.

The following video shows more examples of average word problems:

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