What is the average of the integers from 37 to 195? Here we will show you how to calculate the average of the integers from 37 to 195.
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 37 to 195, we need to divide the sum of the integers from 37 and 195 by the total number of integers from 37 to 195. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 37 to 195 by using a formula where a is the low number of 37 and b is the high number of 195:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((195 - 37 + 1) ÷ 2) × (37 + 195)
Sum = (159 ÷ 2) × (232)
Sum = 79.5 × 232
Sum of Numbers = 18444
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 37 to 195. To calculate the total number of integers, we calculate the difference between 37 and 195 and then add 1. Here is the formula and the math. Once again, a is the low number of 37 and b is the high number of 195:
Total = b - a + 1
Total = 195 - 37 + 1
Total Number = 159
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 37 to 195. 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 = 18444 ÷ 159
Average = 116
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