One-Variable Statistics Question 10

A fish nursery has four tanks for holding fish before they are sold. Twelve fish weighing less than 1 pound are placed in tank A. Twenty-five fish weighing at least 1 pound but no more than 2 pounds are placed in tank B. Nine fish weighting at least 2 pounds but no more than 3 pounds are placed in tank C. Seven fish weighing more than 3 pounds are placed in tank D. Which of the following could be the median of the weight, in pounds, of these 53 fish?

0.3

1.8

2.2

3.5

Approach

We can organize the data into a simple table:

\begin{array}{|c|c|} \hline \text{Weight} & \text{\# of fish} \\ \hline \lt 1 \text{ pound} & 12 \\ \hline \gt 1 \text{ and }\lt 2 \text{ pound} & 25 \\ \hline \gt 2 \text{ and }\lt 3 \text{ pound} & 9 \\ \hline \gt 3 \text{ pound} & 7 \\ \hline \end{array}

Since there are 53 fish in total, the median refers to the 27^th fish. This fish must belong in the $\gt 1 \text{ and } \lt 2 \text{ pound}$ category.