What is the average of even numbers from 100 to 165? Here we will show you how to calculate the average of even numbers from 100 to 165.
To find the average of the even numbers from 100 to 165, we first calculate how many even numbers there are from 100 to 165. Then, we calculate the sum of even numbers from 100 to 165. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 100 to 165, and the even numbers within that range are from 100 to 164. Therefore, the first even number in the sequence is 100, and the last even number in the sequence is 164.
Step 1) Calculate the total number of even numbers from 100 to 165
Here we calculate the total number of even numbers from 100 to 165 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 = (164 - 100 + 2) ÷ 2
tot = 66 ÷ 2
tot = 33
Total even numbers from 100 to 165 = 33
Step 2) Calculate the sum of even numbers from 100 to 165
To calculate the sum of even numbers from 100 to 165, 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 = (33 ÷ 2) × (2 × 100 + (2 × (33 - 1))
sum = 16.5 × (200 + 64)
sum = 16.5 × 264
sum = 4356
Sum of even numbers from 100 to 165 = 4356
Step 3) Calculate the average of even numbers from 100 to 165
Almost done! Now we can calculate the average of even numbers from 100 to 165 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 = 4356 ÷ 33
Average = 132
Average of even numbers from 100 to 165 = 132
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.