What is the average of odd numbers from 31 to 180? Here we will show you how to calculate the average of odd numbers from 31 to 180.
To find the average of the odd numbers from 31 to 180, we first calculate how many odd numbers there are from 31 to 180. Then, we calculate the sum of odd numbers from 31 to 180. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 31 to 180, and the odd numbers within that range are from 31 to 179. Therefore, the first odd number in the sequence is 31, and the last odd number in the sequence is 179.
Step 1) Calculate the total number of odd numbers from 31 to 180
Here we calculate the total number of odd numbers from 31 to 180 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 = (179 - 31 + 2) ÷ 2
tot = 150 ÷ 2
tot = 75
Total odd numbers from 31 to 180 = 75
Step 2) Calculate the sum of odd numbers from 31 to 180
To calculate the sum of odd numbers from 31 to 180, 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 × 31 + (2 × (75 - 1))
sum = 37.5 × (62 + 148)
sum = 37.5 × 210
sum = 7875
Sum of odd numbers from 31 to 180 = 7875
Step 3) Calculate the average of odd numbers from 31 to 180
Almost done! Now we can calculate the average of odd numbers from 31 to 180 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 = 7875 ÷ 75
Average = 105
Average of odd numbers from 31 to 180 = 105
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.