Question

1. consider the following set of data: 5.6, 6.4, 4.0, 1.6, 3.2, 10.6, 6.4, 3.0, 3.0, 3.0 6b determine the outlier. outlier = 10.6 you got it 6c redraw the boxplot after removing the outlier. adjust the edges and whiskers of the boxplot by dragging them to the correct posi lets try that again boxplot image with axis from 0 to 11

Explanation:

Step1: Remove the outlier

The original data set is \(5.6, 6.4, 4.0, 1.6, 3.2, 10.6, 6.4, 3.0, 3.0, 3.0\). After removing the outlier \(10.6\), the new data set is \(1.6, 3.0, 3.0, 3.0, 3.2, 4.0, 5.6, 6.4, 6.4\).

Step2: Find the minimum, Q1, median, Q3, maximum

• Minimum: The smallest value in the new data set is \(1.6\).
• To find Q1, median, Q3: First, sort the data (already sorted: \(1.6, 3.0, 3.0, 3.0, 3.2, 4.0, 5.6, 6.4, 6.4\)). There are 9 data points.
• Median (Q2): The middle value (5th value) is \(3.2\).
• Q1: The median of the lower half (\(1.6, 3.0, 3.0, 3.0\)). There are 4 values, so Q1 is the average of the 2nd and 3rd values: \(\frac{3.0 + 3.0}{2}=3.0\).
• Q3: The median of the upper half (\(4.0, 5.6, 6.4, 6.4\)). There are 4 values, so Q3 is the average of the 2nd and 3rd values: \(\frac{5.6 + 6.4}{2}=6.0\).
• Maximum: The largest value in the new data set is \(6.4\).

Step3: Draw the boxplot

• The box goes from Q1 (\(3.0\)) to Q3 (\(6.0\)), with a line at the median (\(3.2\)).
• The whiskers go from the minimum (\(1.6\)) to Q1 and from Q3 to the maximum (\(6.4\)).

Answer:

The boxplot should have:

• Minimum whisker at \(1.6\)
• Q1 at \(3.0\)
• Median at \(3.2\)
• Q3 at \(6.0\)
• Maximum whisker at \(6.4\)