What is the average of odd numbers from 102 to 193? Here we will show you how to calculate the average of odd numbers from 102 to 193.
To find the average of the odd numbers from 102 to 193, we first calculate how many odd numbers there are from 102 to 193. Then, we calculate the sum of odd numbers from 102 to 193. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 102 to 193, and the odd numbers within that range are from 103 to 193. Therefore, the first odd number in the sequence is 103, and the last odd number in the sequence is 193.
Step 1) Calculate the total number of odd numbers from 102 to 193
Here we calculate the total number of odd numbers from 102 to 193 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 - 103 + 2) ÷ 2
tot = 92 ÷ 2
tot = 46
Total odd numbers from 102 to 193 = 46
Step 2) Calculate the sum of odd numbers from 102 to 193
To calculate the sum of odd numbers from 102 to 193, 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 = (46 ÷ 2) × (2 × 103 + (2 × (46 - 1))
sum = 23 × (206 + 90)
sum = 23 × 296
sum = 6808
Sum of odd numbers from 102 to 193 = 6808
Step 3) Calculate the average of odd numbers from 102 to 193
Almost done! Now we can calculate the average of odd numbers from 102 to 193 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 = 6808 ÷ 46
Average = 148
Average of odd numbers from 102 to 193 = 148
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.