What is the average of odd numbers from 33 to 171? Here we will show you how to calculate the average of odd numbers from 33 to 171.
To find the average of the odd numbers from 33 to 171, we first calculate how many odd numbers there are from 33 to 171. Then, we calculate the sum of odd numbers from 33 to 171. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 33 to 171, and the odd numbers within that range are from 33 to 171. Therefore, the first odd number in the sequence is 33, and the last odd number in the sequence is 171.
Step 1) Calculate the total number of odd numbers from 33 to 171
Here we calculate the total number of odd numbers from 33 to 171 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 = (171 - 33 + 2) ÷ 2
tot = 140 ÷ 2
tot = 70
Total odd numbers from 33 to 171 = 70
Step 2) Calculate the sum of odd numbers from 33 to 171
To calculate the sum of odd numbers from 33 to 171, 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 = (70 ÷ 2) × (2 × 33 + (2 × (70 - 1))
sum = 35 × (66 + 138)
sum = 35 × 204
sum = 7140
Sum of odd numbers from 33 to 171 = 7140
Step 3) Calculate the average of odd numbers from 33 to 171
Almost done! Now we can calculate the average of odd numbers from 33 to 171 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 = 7140 ÷ 70
Average = 102
Average of odd numbers from 33 to 171 = 102
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.