which box plot represents the data? 30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40

Explanation:

Step1: Arrange data in ascending order

$5, 5, 10, 15, 25, 25, 30, 35, 40, 40, 45, 50$

Step2: Find the minimum value

The minimum value is $5$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 12$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{12+ 1}{4}=3.25$. So, $Q_1=10+(15 - 10)\times0.25 = 11.25$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{12 + 1}{2}=6.5$. So, $Q_2=\frac{25+30}{2}=27.5$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(12 + 1)}{4}=9.75$. So, $Q_3=40+(40 - 40)\times0.75 = 40$.

Step6: Find the maximum value

The maximum value is $50$.

Answer:

We need to match the box - plot with minimum value $5$, $Q_1\approx11.25$, median $27.5$, $Q_3 = 40$, and maximum value $50$. Without seeing the visual details of the box - plots clearly, but based on the calculated values, we look for a box - plot with the left - most whisker starting at $5$, the left side of the box around $11.25$, the line in the box around $27.5$, the right side of the box at $40$, and the right - most whisker ending at $50$.