Question

which data set could be represented by the box plot shown below?
choose 1 answer:
a 2,5,7,7,7,8,10,11,11,13,13,14
b 4,5,5,7,7,8,9,9,11,11,13,14
c 4,5,5,7,7,10,10,11,13,13,13,14
d 4,5,7,7,7,8,10,11,11,13,13,14

Explanation:

Step1: Find the minimum value

The minimum value of the box - plot is \(4\). Option A has a minimum value of \(2\), so Option A is incorrect.

Step2: Calculate the first quartile (\(Q_1\))

For a data set with \(n = 12\) data points, \(Q_1\) is the value at the \(\frac{n + 1}{4}=\frac{12+1}{4}=3.25^{th}\) position.
For Option B: The data set is \(4,5,5,7,7,8,9,9,11,11,13,14\). The \(3.25^{th}\) value is \(5+\ 0.25\times(7 - 5)=5 + 0.5=5.5\).
For Option C: The data set is \(4,5,5,7,7,10,10,11,13,13,13,14\). The \(3.25^{th}\) value is \(5+\ 0.25\times(7 - 5)=5 + 0.5=5.5\).
For Option D: The data set is \(4,5,7,7,7,8,10,11,11,13,13,14\). The \(3.25^{th}\) value is \(7+\ 0.25\times(7 - 7)=7\).

Step3: Analyze the box - plot characteristics

In a box - plot, the left - hand side of the box (lower quartile) should match. Since the box - plot seems to have a lower quartile that is consistent with Option D (by visual inspection of the spread and position relative to the minimum value of \(4\) and the overall shape of the box - plot in terms of quartile positions).

Answer:

D. \(4,5,7,7,7,8,10,11,11,13,13,14\)