Question

the data set represents the total number of pencils each student in a class needs to sharpen. 0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9. which box plot correctly represents the data?

Explanation:

Step1: Find the minimum value

The minimum value in the data - set \(0,1,1,1,2,3,4,4,6,6,9\) is \(0\).

Step2: Find the first quartile (Q1)

First, order the data. There are \(n = 11\) data points. The position of Q1 is \(\frac{n + 1}{4}=\frac{11+1}{4}=3\). The 3rd - ordered value is \(1\).

Step3: Find the median (Q2)

The position of the median is \(\frac{n + 1}{2}=\frac{11 + 1}{2}=6\). The 6th - ordered value is \(3\).

Step4: Find the third quartile (Q3)

The position of Q3 is \(\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\). The 9th - ordered value is \(6\).

Step5: Find the maximum value

The maximum value in the data - set is \(9\).

A box - plot has a whisker from the minimum value (\(0\)) to Q1 (\(1\)), a box from Q1 (\(1\)) to Q3 (\(6\)) with a line inside the box at the median (\(3\)), and a whisker from Q3 (\(6\)) to the maximum value (\(9\)).

Answer:

We need to look for a box - plot with a left - most point at \(0\), the left - hand side of the box at \(1\), the line inside the box at \(3\), the right - hand side of the box at \(6\), and the right - most point at \(9\). Without seeing the full details of the options, based on the calculations, the box - plot should have these key features. If we assume the options are standard box - plots with the correct scale, the box - plot that has a left whisker starting at \(0\), box starting at \(1\), median line at \(3\), box ending at \(6\) and right whisker ending at \(9\) is the correct one.