What is the average of even numbers from 71 to 103? Here we will show you how to calculate the average of even numbers from 71 to 103.
To find the average of the even numbers from 71 to 103, we first calculate how many even numbers there are from 71 to 103. Then, we calculate the sum of even numbers from 71 to 103. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 71 to 103, and the even numbers within that range are from 72 to 102. Therefore, the first even number in the sequence is 72, and the last even number in the sequence is 102.
Step 1) Calculate the total number of even numbers from 71 to 103
Here we calculate the total number of even numbers from 71 to 103 by entering the first and last even number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (102 - 72 + 2) ÷ 2
tot = 32 ÷ 2
tot = 16
Total even numbers from 71 to 103 = 16
Step 2) Calculate the sum of even numbers from 71 to 103
To calculate the sum of even numbers from 71 to 103, you enter the total even numbers (tot) from Step 1 and the first even number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (16 ÷ 2) × (2 × 72 + (2 × (16 - 1))
sum = 8 × (144 + 30)
sum = 8 × 174
sum = 1392
Sum of even numbers from 71 to 103 = 1392
Step 3) Calculate the average of even numbers from 71 to 103
Almost done! Now we can calculate the average of even numbers from 71 to 103 by dividing the sum of even numbers from Step 2 by the total even numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 1392 ÷ 16
Average = 87
Average of even numbers from 71 to 103 = 87
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.