What is the average of the integers from 87 to 109? Here we will show you how to calculate the average of the integers from 87 to 109.
To calculate the average of any set of numbers, you divide the sum of the numbers by the total numbers in the set (Sum/Total).
Therefore, to calculate the average of the integers from 87 to 109, we need to divide the sum of the integers from 87 and 109 by the total number of integers from 87 to 109. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 87 to 109 by using a formula where a is the low number of 87 and b is the high number of 109:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((109 - 87 + 1) ÷ 2) × (87 + 109)
Sum = (23 ÷ 2) × (196)
Sum = 11.5 × 196
Sum of Numbers = 2254
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 87 to 109. To calculate the total number of integers, we calculate the difference between 87 and 109 and then add 1. Here is the formula and the math. Once again, a is the low number of 87 and b is the high number of 109:
Total = b - a + 1
Total = 109 - 87 + 1
Total Number = 23
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 87 to 109. We calculate the average of the integers by dividing the Sum of Numbers from Step 1 by the Total Number from Step 2. Here is the math and the answer:
Average = Sum of Numbers ÷ Total Number
Average = 2254 ÷ 23
Average = 98
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