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, 6, 8, 8, 9, 10, 10, 13, 14, 14, 15, 15
min: q1: med: q3: max:
create the box plot by dragging the lines:

Explanation:

Step1: Find Min and Max

The minimum value (Min) is the smallest number in the data set.
The data set is \(6,6,8,8,9,10,10,13,14,14,15,15\). So, \(Min = 6\).
The maximum value (Max) is the largest number in the data set. So, \(Max=15\).

Step2: Find the median (Med)

Since \(n = 12\) (even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values.
\(\frac{n}{2}=6\) and \(\frac{n}{2}+1 = 7\). The 6th value is \(10\) and the 7th value is \(10\).
\(Med=\frac{10 + 10}{2}=10\).

Step3: Find Q1 and Q3

The lower half of the data is \(6,6,8,8,9,10\). Since \(n_1=6\) (even), \(Q1=\frac{8 + 8}{2}=8\).
The upper half of the data is \(13,14,14,15,15\). Since \(n_2 = 6\) (even), \(Q3=\frac{14+14}{2}=14\).

Answer:

Min: \(6\), Q1: \(8\), Med: \(10\), Q3: \(14\), Max: \(15\)