What is the average of even numbers from 21 to 152? Here we will show you how to calculate the average of even numbers from 21 to 152.
To find the average of the even numbers from 21 to 152, we first calculate how many even numbers there are from 21 to 152. Then, we calculate the sum of even numbers from 21 to 152. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 21 to 152, and the even numbers within that range are from 22 to 152. Therefore, the first even number in the sequence is 22, and the last even number in the sequence is 152.
Step 1) Calculate the total number of even numbers from 21 to 152
Here we calculate the total number of even numbers from 21 to 152 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 = (152 - 22 + 2) ÷ 2
tot = 132 ÷ 2
tot = 66
Total even numbers from 21 to 152 = 66
Step 2) Calculate the sum of even numbers from 21 to 152
To calculate the sum of even numbers from 21 to 152, 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 = (66 ÷ 2) × (2 × 22 + (2 × (66 - 1))
sum = 33 × (44 + 130)
sum = 33 × 174
sum = 5742
Sum of even numbers from 21 to 152 = 5742
Step 3) Calculate the average of even numbers from 21 to 152
Almost done! Now we can calculate the average of even numbers from 21 to 152 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 = 5742 ÷ 66
Average = 87
Average of even numbers from 21 to 152 = 87
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.