Question

calculate the values for the 5 - number summary of the skewed dataset 11, 12, 12, 13, 13, 13, 13, 14, 14, 15, 19, 25. (2 points)
the minimum value=
. quartile 1=
. the median=
. quartile 3=
. the maximum value=
.

Explanation:

Step1: Sort the data

First, we have two datasets. Let's consider the second dataset \(11,12,12,13,13,13,14,14,15,19,25\). It is already in ascending order.

Step2: Find the minimum value

The minimum value of a sorted dataset is the first element. For the dataset \(11,12,12,13,13,13,14,14,15,19,25\), the minimum value \(= 11\).

Step3: Find Quartile 1 (\(Q_1\))

The formula for finding \(Q_1\) is \(Q_1=\frac{n + 1}{4}\)th value (when \(n\) is the number of data points). Here \(n = 11\). \(\frac{n+1}{4}=\frac{11 + 1}{4}=3\)rd value. The 3rd value in the dataset \(11,12,12,13,13,13,14,14,15,19,25\) is \(12\). So \(Q_1 = 12\).

Step4: Find the median

The formula for the median (when \(n\) is odd) is \(\frac{n + 1}{2}\)th value. \(\frac{n+1}{2}=\frac{11+1}{2}=6\)th value. The 6th value in the dataset \(11,12,12,13,13,13,14,14,15,19,25\) is \(13\). So the median \(=13\).

Step5: Find Quartile 3 (\(Q_3\))

The formula for \(Q_3\) is \(\frac{3(n + 1)}{4}\)th value. \(\frac{3(n + 1)}{4}=\frac{3\times(11 + 1)}{4}=9\)th value. The 9th value in the dataset \(11,12,12,13,13,13,14,14,15,19,25\) is \(15\). So \(Q_3=15\).

Step6: Find the maximum value

The maximum value of a sorted dataset is the last element. For the dataset \(11,12,12,13,13,13,14,14,15,19,25\), the maximum value \(=25\).

Answer:

Minimum value \(=11\), Quartile 1 \(=12\), Median \(=13\), Quartile 3 \(=15\), Maximum value \(=25\)