Question

select the correct answer. which value is not part of the five - number summary needed for a box plot of this data? {5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} a. 1 b. 5 c. 9 d. 11

Explanation:

Step1: Sort the data

\[1,2,5,6,7,9,12,15,18,19,27\]

Step2: Find the minimum

The minimum value is \(1\).

Step3: Find the first - quartile (\(Q_1\))

There are \(n = 11\) data points. The position of \(Q_1\) is \(\frac{n + 1}{4}=3\). So \(Q_1 = 5\).

Step4: Find the median

The position of the median is \(\frac{n+1}{2}=6\). So the median is \(9\).

Step5: Find the third - quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=9\). So \(Q_3=18\).

Step6: Find the maximum

The maximum value is \(27\).
The five - number summary is \(1,5,9,18,27\).

Answer:

D. 11