What is the average of even numbers from 165 to 180? Here we will show you how to calculate the average of even numbers from 165 to 180.
To find the average of the even numbers from 165 to 180, we first calculate how many even numbers there are from 165 to 180. Then, we calculate the sum of even numbers from 165 to 180. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 165 to 180, and the even numbers within that range are from 166 to 180. Therefore, the first even number in the sequence is 166, and the last even number in the sequence is 180.
Step 1) Calculate the total number of even numbers from 165 to 180
Here we calculate the total number of even numbers from 165 to 180 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 = (180 - 166 + 2) ÷ 2
tot = 16 ÷ 2
tot = 8
Total even numbers from 165 to 180 = 8
Step 2) Calculate the sum of even numbers from 165 to 180
To calculate the sum of even numbers from 165 to 180, 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 = (8 ÷ 2) × (2 × 166 + (2 × (8 - 1))
sum = 4 × (332 + 14)
sum = 4 × 346
sum = 1384
Sum of even numbers from 165 to 180 = 1384
Step 3) Calculate the average of even numbers from 165 to 180
Almost done! Now we can calculate the average of even numbers from 165 to 180 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 = 1384 ÷ 8
Average = 173
Average of even numbers from 165 to 180 = 173
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.