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.
6, 8, 8, 9, 11, 13, 14, 16
min: q1: med: q3: max:
create the box plot by dragging the lines:

Explanation:

Step1: Find Min and Max

The minimum value in the data set \(6,8,8,9,11,13,14,16\) is \(6\). The maximum value is \(16\).

Step2: Find the median (Med)

Since there are \(n = 8\) data points (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). The \(4\)th value is \(9\) and the \(5\)th value is \(11\). So, \(Med=\frac{9 + 11}{2}=\frac{20}{2}=10\).

Step3: Find Q1

The lower - half of the data is \(6,8,8,9\). Since there are \(n_1=4\) data points (even), \(Q1=\frac{8 + 8}{2}=8\).

Step4: Find Q3

The upper - half of the data is \(11,13,14,16\). Since there are \(n_2 = 4\) data points (even), \(Q3=\frac{13+14}{2}=13.5\).

Answer:

Min: \(6\), Q1: \(8\), Med: \(10\), Q3: \(13.5\), Max: \(16\)