What is the average of the integers from 2 to 103? Here we will show you how to calculate the average of the integers from 2 to 103.
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 2 to 103, we need to divide the sum of the integers from 2 and 103 by the total number of integers from 2 to 103. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 2 to 103 by using a formula where a is the low number of 2 and b is the high number of 103:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((103 - 2 + 1) ÷ 2) × (2 + 103)
Sum = (102 ÷ 2) × (105)
Sum = 51 × 105
Sum of Numbers = 5355
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 2 to 103. To calculate the total number of integers, we calculate the difference between 2 and 103 and then add 1. Here is the formula and the math. Once again, a is the low number of 2 and b is the high number of 103:
Total = b - a + 1
Total = 103 - 2 + 1
Total Number = 102
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 2 to 103. 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 = 5355 ÷ 102
Average = 52.5
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