Question

Hammie is in the $6^\text{th}$ grade and weighs $106$ pounds. His quadruplet sisters are tiny babies and weigh $5, 5, 6,$ and $8$ pounds. Which is greater, the average (mean) weight of these five children or the median weight, and by how many pounds?

$\text{median, by } 60$

$\text{median, by } 20$

$\text{average, by } 5$

$\text{average, by } 15$

$\text{average, by } 20$

Video solution:

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Written solution:

The median weight is the middle value, which we can find as: $\cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106}$ Therefore, the median is $6$ pounds.

The average (mean) can be calculated to be: $\begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26. \end{align*}$ This is greater than the median, specifically, the mean is $20$ pounds greater than the median.

Thus, E is the correct answer.

2013 AMC 8 Problem 5

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Problem 5 in Other Years