Question

Billy's basketball team scored the following points over the course of the first $11$ games of the season:

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

If his team scores $40$ in the $12^{\text{th}}$ game, which of the following statistics will show an increase?

$\text{range}$

$\text{median}$

$\text{mean}$

$\text{mode}$

midrange

Video solution:

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Written solution:

When considering all $12$ games, $40$ -- from the $12^{\text{th}}$ game -- will be the lowest score. Therefore, compared to the range of just the first $11$ games, the range of all $12$ games would increase from $73-42 = 31$ to $73-40=33.$

Thus, the correct answer is A .

2015 AMC 8 Problem 5

Video solution:

Written solution:

Problem 5 in Other Years