What is the average of odd numbers from 45 to 194? Here we will show you how to calculate the average of odd numbers from 45 to 194.
To find the average of the odd numbers from 45 to 194, we first calculate how many odd numbers there are from 45 to 194. Then, we calculate the sum of odd numbers from 45 to 194. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 45 to 194, and the odd numbers within that range are from 45 to 193. Therefore, the first odd number in the sequence is 45, and the last odd number in the sequence is 193.
Step 1) Calculate the total number of odd numbers from 45 to 194
Here we calculate the total number of odd numbers from 45 to 194 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 = (193 - 45 + 2) ÷ 2
tot = 150 ÷ 2
tot = 75
Total odd numbers from 45 to 194 = 75
Step 2) Calculate the sum of odd numbers from 45 to 194
To calculate the sum of odd numbers from 45 to 194, 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 = (75 ÷ 2) × (2 × 45 + (2 × (75 - 1))
sum = 37.5 × (90 + 148)
sum = 37.5 × 238
sum = 8925
Sum of odd numbers from 45 to 194 = 8925
Step 3) Calculate the average of odd numbers from 45 to 194
Almost done! Now we can calculate the average of odd numbers from 45 to 194 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 = 8925 ÷ 75
Average = 119
Average of odd numbers from 45 to 194 = 119
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.