What is the average of even numbers from 60 to 178? Here we will show you how to calculate the average of even numbers from 60 to 178.
To find the average of the even numbers from 60 to 178, we first calculate how many even numbers there are from 60 to 178. Then, we calculate the sum of even numbers from 60 to 178. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 60 to 178, and the even numbers within that range are from 60 to 178. Therefore, the first even number in the sequence is 60, and the last even number in the sequence is 178.
Step 1) Calculate the total number of even numbers from 60 to 178
Here we calculate the total number of even numbers from 60 to 178 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 = (178 - 60 + 2) ÷ 2
tot = 120 ÷ 2
tot = 60
Total even numbers from 60 to 178 = 60
Step 2) Calculate the sum of even numbers from 60 to 178
To calculate the sum of even numbers from 60 to 178, 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 = (60 ÷ 2) × (2 × 60 + (2 × (60 - 1))
sum = 30 × (120 + 118)
sum = 30 × 238
sum = 7140
Sum of even numbers from 60 to 178 = 7140
Step 3) Calculate the average of even numbers from 60 to 178
Almost done! Now we can calculate the average of even numbers from 60 to 178 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 = 7140 ÷ 60
Average = 119
Average of even numbers from 60 to 178 = 119
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.