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.
3, 4, 4, 4, 4, 6, 8, 9, 10, 12, 12, 13, 15, 16
min: q1: med: q3: max:
create the box plot by dragging the lines:

Explanation:

Step1: Find Min and Max

The minimum (Min) is the smallest value in the data set. The data set is \(3,4,4,4,4,6,8,9,10,12,12,13,15,16\). So, \(Min = 3\).
The maximum (Max) is the largest value in the data set. So, \(Max=16\).

Step2: Find the median (Med)

The data set has \(n = 14\) values. The median for an even - numbered data set is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=\frac{14}{2}=7\) and \(\frac{n}{2}+1 = 8\). The 7th value is \(8\) and the 8th value is \(9\). So, \(Med=\frac{8 + 9}{2}=8.5\).

Step3: Find Q1

The lower half of the data set is \(3,4,4,4,4,6,8\). This has \(n_1=7\) values. The median of the lower half (Q1) is the \(\frac{n_1 + 1}{2}\)th value. \(\frac{7+1}{2}=4\)th value. The 4th value of the lower - half data set is \(4\). So, \(Q1 = 4\).

Step4: Find Q3

The upper half of the data set is \(10,12,12,13,15,16\). This has \(n_2 = 7\) values. The median of the upper half (Q3) is the \(\frac{n_2+1}{2}\)th value. \(\frac{7 + 1}{2}=4\)th value. The 4th value of the upper - half data set is \(13\). So, \(Q3=13\).

Answer:

Min: \(3\), Q1: \(4\), Med: \(8.5\), Q3: \(13\), Max: \(16\)