which box plot represents the data? 43, 48, 52, 61, 74, 81, 40, 42, 56, 77, 81, 43

Explanation:

Step1: Sort the data

$40,42,43,43,48,52,56,61,74,77,81,81$

Step2: Find the minimum value

The minimum value is $40$.

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, $Q_1=43$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{12 + 1}{2}=6.5$. So, $Q_2=\frac{52 + 56}{2}=54$.

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, $Q_3=74$.

Step6: Find the maximum value

The maximum value is $81$.

Answer:

We need to match the box - plot with a minimum of $40$, $Q_1 = 43$, median of $54$, $Q_3=74$, and maximum of $81$. Without seeing the specific details of each box - plot option in a clear way (since no labels are given for each option), we would look for a box - plot where the left - most whisker starts at $40$, the left side of the box is at $43$, the line inside the box is at $54$, the right side of the box is at $74$, and the right - most whisker ends at $81$.