What is the average of even numbers from 11 to 78? Here we will show you how to calculate the average of even numbers from 11 to 78.
To find the average of the even numbers from 11 to 78, we first calculate how many even numbers there are from 11 to 78. Then, we calculate the sum of even numbers from 11 to 78. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 11 to 78, and the even numbers within that range are from 12 to 78. Therefore, the first even number in the sequence is 12, and the last even number in the sequence is 78.
Step 1) Calculate the total number of even numbers from 11 to 78
Here we calculate the total number of even numbers from 11 to 78 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 = (78 - 12 + 2) ÷ 2
tot = 68 ÷ 2
tot = 34
Total even numbers from 11 to 78 = 34
Step 2) Calculate the sum of even numbers from 11 to 78
To calculate the sum of even numbers from 11 to 78, 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 = (34 ÷ 2) × (2 × 12 + (2 × (34 - 1))
sum = 17 × (24 + 66)
sum = 17 × 90
sum = 1530
Sum of even numbers from 11 to 78 = 1530
Step 3) Calculate the average of even numbers from 11 to 78
Almost done! Now we can calculate the average of even numbers from 11 to 78 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 = 1530 ÷ 34
Average = 45
Average of even numbers from 11 to 78 = 45
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.