What is the average of odd numbers from 8 to 163? Here we will show you how to calculate the average of odd numbers from 8 to 163.
To find the average of the odd numbers from 8 to 163, we first calculate how many odd numbers there are from 8 to 163. Then, we calculate the sum of odd numbers from 8 to 163. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 8 to 163, and the odd numbers within that range are from 9 to 163. Therefore, the first odd number in the sequence is 9, and the last odd number in the sequence is 163.
Step 1) Calculate the total number of odd numbers from 8 to 163
Here we calculate the total number of odd numbers from 8 to 163 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 = (163 - 9 + 2) ÷ 2
tot = 156 ÷ 2
tot = 78
Total odd numbers from 8 to 163 = 78
Step 2) Calculate the sum of odd numbers from 8 to 163
To calculate the sum of odd numbers from 8 to 163, 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 = (78 ÷ 2) × (2 × 9 + (2 × (78 - 1))
sum = 39 × (18 + 154)
sum = 39 × 172
sum = 6708
Sum of odd numbers from 8 to 163 = 6708
Step 3) Calculate the average of odd numbers from 8 to 163
Almost done! Now we can calculate the average of odd numbers from 8 to 163 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 = 6708 ÷ 78
Average = 86
Average of odd numbers from 8 to 163 = 86
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.