What is the average of odd numbers from 45 to 186? Here we will show you how to calculate the average of odd numbers from 45 to 186.
To find the average of the odd numbers from 45 to 186, we first calculate how many odd numbers there are from 45 to 186. Then, we calculate the sum of odd numbers from 45 to 186. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 45 to 186, and the odd numbers within that range are from 45 to 185. Therefore, the first odd number in the sequence is 45, and the last odd number in the sequence is 185.
Step 1) Calculate the total number of odd numbers from 45 to 186
Here we calculate the total number of odd numbers from 45 to 186 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 = (185 - 45 + 2) ÷ 2
tot = 142 ÷ 2
tot = 71
Total odd numbers from 45 to 186 = 71
Step 2) Calculate the sum of odd numbers from 45 to 186
To calculate the sum of odd numbers from 45 to 186, 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 = (71 ÷ 2) × (2 × 45 + (2 × (71 - 1))
sum = 35.5 × (90 + 140)
sum = 35.5 × 230
sum = 8165
Sum of odd numbers from 45 to 186 = 8165
Step 3) Calculate the average of odd numbers from 45 to 186
Almost done! Now we can calculate the average of odd numbers from 45 to 186 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 = 8165 ÷ 71
Average = 115
Average of odd numbers from 45 to 186 = 115
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.