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:

1. Discipline and Sub - field:

• The problem involves analyzing a data - set and representing it using a box - plot. This falls under the discipline of Mathematics, specifically the sub - field of Statistics.

1. Steps to find the correct box - plot:

• First, find the five - number summary of the data set \(0,1,1,1,2,3,4,4,6,6,9\).
• Minimum: The minimum value in the data set is \(0\).
• First quartile (Q1): There are \(n = 11\) data points. The position of Q1 is \(\frac{n + 1}{4}=\frac{11+1}{4}=3\). So, Q1 is the 3rd ordered data - point, which is \(1\).
• Median (Q2): The position of the median is \(\frac{n + 1}{2}=\frac{11 + 1}{2}=6\). So, the median is the 6th ordered data - point, which is \(3\).
• Third quartile (Q3): The position of Q3 is \(\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\). So, Q3 is the 9th ordered data - point, which is \(6\).
• Maximum: The maximum value in the data set is \(9\).
• A box - plot has a box from Q1 to Q3 with a line at the median inside the box, and whiskers from the box to the minimum and maximum values.
• The box should start at \(1\), end at \(6\), have a line at \(3\) inside the box, and whiskers going to \(0\) and \(9\).

Since you did not provide the option labels, we assume the first box - plot with the following characteristics is correct: The box starts at \(1\), ends at \(6\), has a vertical line inside the box at \(3\), and whiskers extend to \(0\) and \(9\).

Answer:

The box - plot with a box starting at 1, ending at 6, a vertical line at 3 inside the box, and whiskers extending to 0 and 9.