Skill Builder: No Computation Method to Find Mean of Consecutive Numbers

The SHSAT sometimes requires us to figure out the sum of consecutive numbers. Here is an example from the SHSAT Practic Test 5 (Old Format).

Question 62. Given: n is an even integer and 10 < n < 19. What is the mean of all possible values of n?

F) 14

G) 14.5

H) 15

J) 15.5

K) 30

We know that all possible values of n are: {12, 14, 16, 18}.

To calculate the mean, we can simply add the four values for n, and then divide that sum by 4. But, did you know that there is a method to find the mean that requires no computation at all?

Since the four possible values of n happen also to be consecutive numbers--in this case, consecutive even integers--we can simply apply the following special trait that applies to any set of consecutive numbers.

With any set of consecutive numbers, the mean of that set is equal to the median.

This means that we simply have to locate the median for the above values of n, and we'll find the mean. In this case, the median of all possible values of n is 15 because it is the number in the middle position--between 14 and 16-- of the given set.

There is no need to add or divide anything. Here it is again:

In a set of consecutive numbers, the mean = the median.

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