What is the average of the integers from 1 to 199? Here we will show you how to calculate the average of the integers from 1 to 199.
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 199, we need to divide the sum of the integers from 1 and 199 by the total number of integers from 1 to 199. 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 199 by using a formula where a is the low number of 1 and b is the high number of 199:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((199 - 1 + 1) ÷ 2) × (1 + 199)
Sum = (199 ÷ 2) × (200)
Sum = 99.5 × 200
Sum of Numbers = 19900
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 1 to 199. To calculate the total number of integers, we calculate the difference between 1 and 199 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 199:
Total = b - a + 1
Total = 199 - 1 + 1
Total Number = 199
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 1 to 199. 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 = 19900 ÷ 199
Average = 100
Average of Integers in a Sequence Calculator
Use this calculator to calculate the average of integers in a sequence.