Question

gabe is the human resources manager for the advanced scientific research lab. he has to record the heights (in centimeters) and weights (in pounds) for each of the scientists in the lab.

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$$\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \\hline height distribution (cm) & 178 & 163 & 174 & 186 & 154 & 167 & 167 & 181 & 159 & 165 & 177 & 191 & 158 \\\\ \\hline weight distribution (lbs) & 157 & 163 & 190 & 187 & 183 & 173 & 184 & 189 & 193 & 192 & 177 & 173 & 168 \\\\ \\hline \\end{tabular}$$

select the correct answer.

what are the medians for the height and weight distribution, respectively?

170, 179
183, 167
167, 183
179, 170
165, 175

Explanation:

Sort height data and find median

The height data set contains \(n = 13\) values:

$$ \{178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158\} $$

Sorting in ascending order:

$$ \{154, 158, 159, 163, 165, 167, 167, 174, 177, 178, 181, 186, 191\} $$

Since \(n = 13\) is odd, the median is the \(7^{\text{th}}\) value:

$$ \text{Median}_{\text{height}} = 167 $$

Sort weight data and find median

The weight data set contains \(n = 13\) values:

$$ \{157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168\} $$

Sorting in ascending order:

$$ \{157, 163, 168, 173, 173, 177, 183, 184, 187, 189, 190, 192, 193\} $$

Since \(n = 13\) is odd, the median is the \(7^{\text{th}}\) value:

$$ \text{Median}_{\text{weight}} = 183 $$

Identify the correct option

The medians for height and weight are \(167\) and \(183\), respectively.

Answer:

• 170, 179
• 183, 167
• 167, 183 (Correct answer)
• 179, 170
• 165, 175