Answer:
Option D is the correct choice.
Explanation:
We have been given a data set representing the total number of pencils each student in a class needs to sharpen as:
0, 1, 1, 1, 2, 3, 4, 4, 6, 6, 9
Let us find median of our given data set. As our data set has 11 data points, so median will be the value of 6th data point, that is 3.
Since first quartile is the median of the lower half of the data. Let us find our lower quartile. Since there are 5 data points below median, so our lower quartile will be the value of 3rd data point, that is 1.
Upper or 3rd quartile is the median of the upper half of the data. Since there are 5 data points above median, so our upper quartile will be the value of 9th data point, that is 6.
We can see that box plot represented by option D is the correct choice as middle line of box is at 3, which represents median of our data set. Lower quartile is at 1 and upper quartile is at 6.
Therefore, box plot shown in option D correctly represents the data.