What is the average of odd numbers from 31 to 106? Here we will show you how to calculate the average of odd numbers from 31 to 106.
To find the average of the odd numbers from 31 to 106, we first calculate how many odd numbers there are from 31 to 106. Then, we calculate the sum of odd numbers from 31 to 106. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 31 to 106, and the odd numbers within that range are from 31 to 105. Therefore, the first odd number in the sequence is 31, and the last odd number in the sequence is 105.
Step 1) Calculate the total number of odd numbers from 31 to 106
Here we calculate the total number of odd numbers from 31 to 106 by entering the first and last odd number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (105 - 31 + 2) ÷ 2
tot = 76 ÷ 2
tot = 38
Total odd numbers from 31 to 106 = 38
Step 2) Calculate the sum of odd numbers from 31 to 106
To calculate the sum of odd numbers from 31 to 106, you enter the total odd numbers (tot) from Step 1 and the first odd number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (38 ÷ 2) × (2 × 31 + (2 × (38 - 1))
sum = 19 × (62 + 74)
sum = 19 × 136
sum = 2584
Sum of odd numbers from 31 to 106 = 2584
Step 3) Calculate the average of odd numbers from 31 to 106
Almost done! Now we can calculate the average of odd numbers from 31 to 106 by dividing the sum of odd numbers from Step 2 by the total odd numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 2584 ÷ 38
Average = 68
Average of odd numbers from 31 to 106 = 68
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.