Question

which box plot represents the data set given? 10, 12, 14, 15, 16, 18, 21, 24, 27, 30 choose the correct answer.

Explanation:

Step1: Find the minimum value

The minimum value of the data - set 10, 12, 14, 15, 16, 18, 21, 24, 27, 30 is 10.

Step2: Find the first quartile ($Q_1$)

The data - set has $n = 10$ values. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{10+1}{4}=2.75$. So, $Q_1$ is the value at the 2.75th position. Interpolating between the 2nd and 3rd ordered values: $Q_1=12+(14 - 12)\times0.75 = 13.5$.

Step3: Find the median ($Q_2$)

The position of the median for $n = 10$ values is $\frac{n+1}{2}=5.5$. Interpolating between the 5th and 6th ordered values: $Q_2=\frac{16 + 18}{2}=17$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(10 + 1)}{4}=8.25$. Interpolating between the 8th and 9th ordered values: $Q_3=24+(27 - 24)\times0.25=24.75$.

Step5: Find the maximum value

The maximum value of the data - set is 30.

Answer:

We need to check which box - plot has a minimum of 10, $Q_1\approx13.5$, $Q_2 = 17$, $Q_3\approx24.75$, and a maximum of 30. Without seeing the visual details of the box - plots in a clear way to compare these values exactly, we assume the correct box - plot will have the left - most point at 10, the left side of the box around 13.5, the line in the box at 17, the right side of the box around 24.75, and the right - most point at 30. If we had to make a choice based on these calculated values, we would look for the box - plot that matches these characteristics. Since no specific visual evaluation can be done here just from the text description of the box - plots, we have completed the numerical part of analyzing the data for the box - plot. If you can provide more details about the box - plots' visual features, a more definite answer can be given.