What is the average of odd numbers from 21 to 83? Here we will show you how to calculate the average of odd numbers from 21 to 83.
To find the average of the odd numbers from 21 to 83, we first calculate how many odd numbers there are from 21 to 83. Then, we calculate the sum of odd numbers from 21 to 83. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 21 to 83, and the odd numbers within that range are from 21 to 83. Therefore, the first odd number in the sequence is 21, and the last odd number in the sequence is 83.
Step 1) Calculate the total number of odd numbers from 21 to 83
Here we calculate the total number of odd numbers from 21 to 83 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 = (83 - 21 + 2) ÷ 2
tot = 64 ÷ 2
tot = 32
Total odd numbers from 21 to 83 = 32
Step 2) Calculate the sum of odd numbers from 21 to 83
To calculate the sum of odd numbers from 21 to 83, 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 = (32 ÷ 2) × (2 × 21 + (2 × (32 - 1))
sum = 16 × (42 + 62)
sum = 16 × 104
sum = 1664
Sum of odd numbers from 21 to 83 = 1664
Step 3) Calculate the average of odd numbers from 21 to 83
Almost done! Now we can calculate the average of odd numbers from 21 to 83 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 = 1664 ÷ 32
Average = 52
Average of odd numbers from 21 to 83 = 52
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.