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 Minimum (Min)

The minimum value is the smallest number in the data set. Looking at the data \(3,4,4,4,4,6,8,9,10,12,12,13,15,16\), the smallest number is \(3\).

Step2: Find Quartile 1 (Q1)

First, find the median (Med) to split the data into lower and upper halves. The data set has \(n = 14\) values. The median is the average of the \(7^{th}\) and \(8^{th}\) values. The \(7^{th}\) value is \(8\) and the \(8^{th}\) value is \(9\), so \(Med=\frac{8 + 9}{2}=8.5\). The lower half of the data is \(3,4,4,4,4,6,8\) (first 7 values). The median of the lower half (Q1) is the \(4^{th}\) value, which is \(4\).

Step3: Find Median (Med)

As calculated above, with \(n = 14\), the median is the average of the \(7^{th}\) (\(8\)) and \(8^{th}\) (\(9\)) values: \(Med=\frac{8+9}{2}=8.5\).

Step4: Find Quartile 3 (Q3)

The upper half of the data is \(9,10,12,12,13,15,16\) (last 7 values). The median of the upper half (Q3) is the \(4^{th}\) value of this sub - set. The sub - set is \(9,10,12,12,13,15,16\), and the \(4^{th}\) value is \(12\).

Step5: Find Maximum (Max)

The maximum value is the largest number in the data set. In \(3,4,4,4,4,6,8,9,10,12,12,13,15,16\), the largest number is \(16\).

Answer:

Min: \(3\)
Q1: \(4\)
Med: \(8.5\)
Q3: \(12\)
Max: \(16\)

For the box - and - whisker plot:

• The left whisker starts at the minimum value (\(3\)) and ends at Q1 (\(4\)).
• The left side of the box is at Q1 (\(4\)), the line inside the box is at the median (\(8.5\)), and the right side of the box is at Q3 (\(12\)).
• The right whisker starts at Q3 (\(12\)) and ends at the maximum value (\(16\)).