Question

which set of data is displayed in the box plot shown below?
a 2, 3, 4, 5, 5, 6, 7, 7, 8, 10
b 2, 2, 3, 4, 4, 4, 5, 6, 8, 10
c 2, 2, 4, 5, 5, 6, 6, 6, 9, 10
d 2, 2, 4, 4, 5, 5, 7, 7, 8, 10
a
b
c
d

Explanation:

Step1: Determine the minimum and maximum values

A box - plot shows the minimum, first quartile (\(Q_1\)), median (\(Q_2\)), third quartile (\(Q_3\)), and maximum values. The left - most point is the minimum and the right - most point is the maximum. From the box - plot, the minimum value is \(2\) and the maximum value is \(10\). All the options A, B, C, D have a minimum of \(2\) and a maximum of \(10\).

Step2: Check the symmetry and distribution

We can also check the spread of the data. Let's consider the number of data points. Each option has \(10\) data points.
For option D: \(2,2,4,4,5,5,7,7,8,10\)
The median (\(Q_2\)) of a set with \(n = 10\) data points (where \(n\) is even) is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. The \(\frac{10}{2}=5\)th and \(6\)th values are \(5\) and \(5\), so \(Q_2=\frac{5 + 5}{2}=5\)
The first quartile (\(Q_1\)) is the median of the first \(5\) values. The first \(5\) values \(2,2,4,4,5\), and \(Q_1 = 4\)
The third quartile (\(Q_3\)) is the median of the last \(5\) values. The last \(5\) values \(5,7,7,8,10\), and \(Q_3=7\)

For option A: \(2,3,4,5,5,6,7,7,8,10\)
The median (\(Q_2\)): \(\frac{5+6}{2}=5.5\)
For option B: \(2,2,3,4,4,4,5,6,8,10\)
The median (\(Q_2\)): \(\frac{4 + 4}{2}=4\)
For option C: \(2,2,4,5,5,6,6,6,9,10\)
The median (\(Q_2\)): \(\frac{5+6}{2}=5.5\)

Answer:

D. \(2,2,4,4,5,5,7,7,8,10\)