2015 AMC 8

Complete problem set with solutions and individual problem pages

Problem 5 Easy

Billy's basketball team scored the following points over the course of the first 11 games of the season. If his team scores 40 in the 12^{th} game, which of the following statistics will show an increase?

42, 47, 53, 53, 58, 58, 58, 61, 64, 65, 73

  • A.

    \text{range}

  • B.

    \text{median}

  • C.

    \text{mean}

  • D.

    \text{mode}

  • E.

    \text{mid-range}

Answer:A

Solution 1

When they score a 40 on the next game, the range increases from 73-42=31 to 73-40=33. This means the \boxed{\textbf{(A) } \text{range}} increased.

Note: The range is defined to be the difference of the largest element and the smallest element of a set.

 

Solution 2

Because 40 is less than the score of every game they've played so far, the measures of center will never rise. Only measures of spread, such as the \boxed{\textbf{(A)}~\text{range}}, may increase.

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