What is the average of odd numbers from 45 to 192? Here we will show you how to calculate the average of odd numbers from 45 to 192.
To find the average of the odd numbers from 45 to 192, we first calculate how many odd numbers there are from 45 to 192. Then, we calculate the sum of odd numbers from 45 to 192. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 45 to 192, and the odd numbers within that range are from 45 to 191. Therefore, the first odd number in the sequence is 45, and the last odd number in the sequence is 191.
Step 1) Calculate the total number of odd numbers from 45 to 192
Here we calculate the total number of odd numbers from 45 to 192 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 = (191 - 45 + 2) ÷ 2
tot = 148 ÷ 2
tot = 74
Total odd numbers from 45 to 192 = 74
Step 2) Calculate the sum of odd numbers from 45 to 192
To calculate the sum of odd numbers from 45 to 192, 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 = (74 ÷ 2) × (2 × 45 + (2 × (74 - 1))
sum = 37 × (90 + 146)
sum = 37 × 236
sum = 8732
Sum of odd numbers from 45 to 192 = 8732
Step 3) Calculate the average of odd numbers from 45 to 192
Almost done! Now we can calculate the average of odd numbers from 45 to 192 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 = 8732 ÷ 74
Average = 118
Average of odd numbers from 45 to 192 = 118
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.