The average (arithmetic mean) uses the formula:
The formula can also be written as
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?
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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