What is the average of odd numbers from 47 to 198? Here we will show you how to calculate the average of odd numbers from 47 to 198.
To find the average of the odd numbers from 47 to 198, we first calculate how many odd numbers there are from 47 to 198. Then, we calculate the sum of odd numbers from 47 to 198. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 47 to 198, and the odd numbers within that range are from 47 to 197. Therefore, the first odd number in the sequence is 47, and the last odd number in the sequence is 197.
Step 1) Calculate the total number of odd numbers from 47 to 198
Here we calculate the total number of odd numbers from 47 to 198 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 = (197 - 47 + 2) ÷ 2
tot = 152 ÷ 2
tot = 76
Total odd numbers from 47 to 198 = 76
Step 2) Calculate the sum of odd numbers from 47 to 198
To calculate the sum of odd numbers from 47 to 198, 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 = (76 ÷ 2) × (2 × 47 + (2 × (76 - 1))
sum = 38 × (94 + 150)
sum = 38 × 244
sum = 9272
Sum of odd numbers from 47 to 198 = 9272
Step 3) Calculate the average of odd numbers from 47 to 198
Almost done! Now we can calculate the average of odd numbers from 47 to 198 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 = 9272 ÷ 76
Average = 122
Average of odd numbers from 47 to 198 = 122
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.