What is the average (arithmetic mean) of all multiples of 10 from 10 to 200 inclusive?
What is the average (arithmetic mean) of all multiples of 10 from 10 to 200 inclusive?
Answer/Solution
105
Steps/Work
This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 200, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
20(10) = 200
So we know that there are 40 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 200 = 210
20 + 190 = 210
30 + 180 = 210
Etc.
Since there are 20 total terms, this pattern will create 10 'pairs' of 210.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(10)(210)/(20) =105
Answer : B
We're asked for the average of all of the multiples of 10 from 10 to 200, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
20(10) = 200
So we know that there are 40 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 200 = 210
20 + 190 = 210
30 + 180 = 210
Etc.
Since there are 20 total terms, this pattern will create 10 'pairs' of 210.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(10)(210)/(20) =105
Answer : B