Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals.
4,4,5,6,6,11,11,13,14,14,16,16
min: 4 q1: med: q3: max: 1
create the box plot by dragging the lines:

Explanation:

Step1: Find the median (Med)

The data set has \(n = 12\) values. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{12}{2}=6\) and \(\frac{12}{2}+1 = 7\). The 6th value is \(11\) and the 7th value is \(11\). So, \(Med=\frac{11 + 11}{2}=11\).

Step2: Find \(Q1\)

The lower - half of the data is \(4,4,5,6,6,11\). The number of values in the lower - half \(n_1=6\). The median of the lower - half (\(Q1\)) is the average of the \(\frac{n_1}{2}\)th and \((\frac{n_1}{2}+1)\)th values. \(\frac{6}{2}=3\) and \(\frac{6}{2}+1 = 4\). The 3rd value is \(5\) and the 4th value is \(6\). So, \(Q1=\frac{5 + 6}{2}=5.5\).

Step3: Find \(Q3\)

The upper - half of the data is \(11,13,14,14,16,16\). The number of values in the upper - half \(n_2 = 6\). The median of the upper - half (\(Q3\)) is the average of the \(\frac{n_2}{2}\)th and \((\frac{n_2}{2}+1)\)th values. \(\frac{6}{2}=3\) and \(\frac{6}{2}+1 = 4\). The 3rd value is \(14\) and the 4th value is \(14\). So, \(Q3=\frac{14+14}{2}=14\).

Step4: Find the maximum (Max)

By looking at the data set \(4,4,5,6,6,11,11,13,14,14,16,16\), the maximum value \(Max = 16\).

Answer:

\(Q1 = 5.5\), \(Med=11\), \(Q3 = 14\), \(Max = 16\)