Question

choose all of the box plots that correctly displays the data

Explanation:

Step1: Order the data

First, order each set of data. For example, for the data in option A: 12, 15, 15, 15, 18, 18, 20, 20, 24, 27.

Step2: Find the median

The median of a set with \(n\) values (where \(n = 10\) here) is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+ 1)\) - th ordered values. For \(n = 10\), the median is the average of the 5 - th and 6 - th values. In option A, the median is \(\frac{18 + 18}{2}=18\).

Step3: Find the lower and upper quartiles

The lower half of the data for option A is 12, 15, 15, 15, 18. The median of the lower half (lower - quartile \(Q_1\)) is 15. The upper half of the data is 18, 20, 20, 24, 27. The median of the upper half (upper - quartile \(Q_3\)) is 20.

Step4: Check box - plot features

The box in a box - plot goes from \(Q_1\) to \(Q_3\), the line inside the box is the median, and the whiskers extend to the minimum and maximum non - outlier values.
For option A:

• Minimum value is 12.
• \(Q_1 = 15\), median = 18, \(Q_3 = 20\), maximum value is 27. The box - plot in option A correctly represents these values.

For option B:

• Order the data: 14, 16, 20, 24, 25, 27, 28. \(n = 7\), median is the 4 - th value, which is 24. \(Q_1\) is the median of 14, 16, 20 (i.e., 16), \(Q_3\) is the median of 25, 27, 28 (i.e., 27). The box - plot does not match these values.

For option C:

• Order the data: 10, 12, 12, 12, 13, 18, 25, 26. \(n = 8\), median is \(\frac{12+13}{2}=12.5\), \(Q_1\) is 12, \(Q_3\) is 18. The box - plot does not match these values.

For option D:

• Order the data: 11, 18, 22, 25, 27, 28, 29. \(n = 7\), median is 22, \(Q_1\) is 18, \(Q_3\) is 27. The box - plot does not match these values.

Answer:

A. Option A