What is the average of the integers from 3 to 30? Here we will show you how to calculate the average of the integers from 3 to 30.
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 3 to 30, we need to divide the sum of the integers from 3 and 30 by the total number of integers from 3 to 30. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 3 to 30 by using a formula where a is the low number of 3 and b is the high number of 30:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((30 - 3 + 1) ÷ 2) × (3 + 30)
Sum = (28 ÷ 2) × (33)
Sum = 14 × 33
Sum of Numbers = 462
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 3 to 30. To calculate the total number of integers, we calculate the difference between 3 and 30 and then add 1. Here is the formula and the math. Once again, a is the low number of 3 and b is the high number of 30:
Total = b - a + 1
Total = 30 - 3 + 1
Total Number = 28
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 3 to 30. 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 = 462 ÷ 28
Average = 16.5
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