What is the average of the integers from 1 to 101? Here we will show you how to calculate the average of the integers from 1 to 101.
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 1 to 101, we need to divide the sum of the integers from 1 and 101 by the total number of integers from 1 to 101. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 1 to 101 by using a formula where a is the low number of 1 and b is the high number of 101:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((101 - 1 + 1) ÷ 2) × (1 + 101)
Sum = (101 ÷ 2) × (102)
Sum = 50.5 × 102
Sum of Numbers = 5151
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 1 to 101. To calculate the total number of integers, we calculate the difference between 1 and 101 and then add 1. Here is the formula and the math. Once again, a is the low number of 1 and b is the high number of 101:
Total = b - a + 1
Total = 101 - 1 + 1
Total Number = 101
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 1 to 101. 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 = 5151 ÷ 101
Average = 51
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