Question

ian sells his drawings at weekend art fairs. he recorded how much he earned each weekend for the past few months. amount earned ($) 120 200 100 180 150 120 165 180 100 which box plot represents the data?

Explanation:

Step1: Order the data

$100,100,120,120,150,165,180,180,200$

Step2: Find the minimum value

The minimum value is $100$.

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

There are 9 data points. The position of $Q_1$ is $\frac{1 + 9}{4}=2.5$. So, $Q_1=\frac{100 + 120}{2}=110$.

Step4: Find the median ($Q_2$)

The median is the 5th - ordered value. So, $Q_2 = 150$.

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

The position of $Q_3$ is $\frac{3\times(1 + 9)}{4}=7.5$. So, $Q_3=\frac{180+180}{2}=180$.

Step6: Find the maximum value

The maximum value is $200$.

The box - plot should have the left - most whisker at $100$, the left side of the box at $110$, the line in the box at $150$, the right side of the box at $180$, and the right - most whisker at $200$.

Answer:

We need to match the calculated values of minimum ($100$), $Q_1$ ($110$), median ($150$), $Q_3$ ($180$), and maximum ($200$) with the given box - plots. Without the full set of box - plot options shown completely, we know the correct box - plot should have the box starting around $110$, the vertical line in the box at $150$, the box ending at $180$, and whiskers from $100$ to $200$.