What is the average of even numbers from 50 to 198? Here we will show you how to calculate the average of even numbers from 50 to 198.
To find the average of the even numbers from 50 to 198, we first calculate how many even numbers there are from 50 to 198. Then, we calculate the sum of even numbers from 50 to 198. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 50 to 198, and the even numbers within that range are from 50 to 198. Therefore, the first even number in the sequence is 50, and the last even number in the sequence is 198.
Step 1) Calculate the total number of even numbers from 50 to 198
Here we calculate the total number of even numbers from 50 to 198 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 = (198 - 50 + 2) ÷ 2
tot = 150 ÷ 2
tot = 75
Total even numbers from 50 to 198 = 75
Step 2) Calculate the sum of even numbers from 50 to 198
To calculate the sum of even numbers from 50 to 198, 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 = (75 ÷ 2) × (2 × 50 + (2 × (75 - 1))
sum = 37.5 × (100 + 148)
sum = 37.5 × 248
sum = 9300
Sum of even numbers from 50 to 198 = 9300
Step 3) Calculate the average of even numbers from 50 to 198
Almost done! Now we can calculate the average of even numbers from 50 to 198 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 = 9300 ÷ 75
Average = 124
Average of even numbers from 50 to 198 = 124
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.