Question

topic: measures of center
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
which box - and - whisker plot represents this data: 6, 7, 8, 10, 18, 20, 22, 25, 28, 28, 30, 30?

Explanation:

Step1: Find the minimum value

The minimum value of the data - set \(6,7,8,10,18,20,22,25,28,28,30,30\) is \(6\).

Step2: Find the first - quartile (\(Q_1\))

The data - set has \(n = 12\) values. The lower half of the data is \(6,7,8,10,18,20\). The median of the lower half (\(Q_1\)) is \(\frac{8 + 10}{2}=9\).

Step3: Find the median (\(Q_2\))

Since \(n = 12\) (an even number of data points), the median \(Q_2=\frac{20 + 22}{2}=21\).

Step4: Find the third - quartile (\(Q_3\))

The upper half of the data is \(22,25,28,28,30,30\). The median of the upper half (\(Q_3\)) is \(\frac{28+28}{2}=28\).

Step5: Find the maximum value

The maximum value of the data - set is \(30\).
A box - and - whisker plot has the minimum value at the left - most end of the left whisker, \(Q_1\) at the left end of the box, the median at the line inside the box, \(Q_3\) at the right end of the box, and the maximum value at the right - most end of the right whisker.
We look for a box - and - whisker plot with the left - most point at \(6\), the left side of the box around \(9\), the line in the box around \(21\), the right side of the box around \(28\), and the right - most point at \(30\).

Answer:

(The correct box - and - whisker plot is the one that has the minimum value at \(6\), \(Q_1\approx9\), median \(\approx21\), \(Q_3\approx28\), and maximum value at \(30\). Since the options are not labeled, you would need to visually inspect which plot has these characteristics.)