Mean of first 10 even numbers
Probability
Level
1
What is the mean of the first 10 positive even numbers?
10
11
12
13
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1 solution
The first 10 positive even numbers are
2 , 4 , 6 , 8 , 1 0 , 1 2 , 1 4 , 1 6 , 1 8 , 2 0 .
Solution 1: Observe that we can pair off this set from the front and the back, to get sets with sum of 22. Specifically, 2 + 2 0 = 2 2 , 4 + 1 8 = 2 2 , 6 + 1 6 = 2 2 , 8 + 1 4 = 2 2 , 1 0 + 1 2 = 2 2 . This tells us that their mean is 2 2 2 = 1 1 .
Solution 2: The mean of a set is their average. Hence, their mean is
1 0 2 + 4 + 6 + 8 + 1 0 + 1 2 + 1 4 + 1 6 + 1 8 + 2 0 = 1 1 .