What is the average of the integers from 100 to 200? Here we will show you how to calculate the average of the integers from 100 to 200.
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 100 to 200, we need to divide the sum of the integers from 100 and 200 by the total number of integers from 100 to 200. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 100 to 200 by using a formula where a is the low number of 100 and b is the high number of 200:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((200 - 100 + 1) ÷ 2) × (100 + 200)
Sum = (101 ÷ 2) × (300)
Sum = 50.5 × 300
Sum of Numbers = 15150
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 100 to 200. To calculate the total number of integers, we calculate the difference between 100 and 200 and then add 1. Here is the formula and the math. Once again, a is the low number of 100 and b is the high number of 200:
Total = b - a + 1
Total = 200 - 100 + 1
Total Number = 101
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 100 to 200. 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 = 15150 ÷ 101
Average = 150
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