Question

1. consider the following set of data:

2.0, 12.8, 3.2, 4.0, 2.8, 6.6, 5.8, 6.6, 2.8, 2.8
11b determine the outlier.
outlier = 12.8
...
11c redraw the boxplot after removing the outlier. adjust the edges and whiskers of the boxplot by dragging them to the correct positions.
boxplot image with number line 0–13

Explanation:

Step1: Remove the outlier

The outlier is 12.8, so the new data set is: 2.0, 3.2, 4.0, 2.8, 6.6, 5.8, 6.6, 2.8, 2.8.

Step2: Sort the data

Sort the new data set: 2.0, 2.8, 2.8, 2.8, 3.2, 4.0, 5.8, 6.6, 6.6.

Step3: Find the minimum, Q1, median, Q3, maximum

• Minimum: 2.0
• Q1 (25th percentile): The median of the lower half (2.0, 2.8, 2.8, 2.8). The lower half has 4 values, so Q1 is the average of the 2nd and 3rd values: $\frac{2.8 + 2.8}{2} = 2.8$.
• Median (50th percentile): The middle value of the 9 - value data set, which is the 5th value: 3.2.
• Q3 (75th percentile): The median of the upper half (4.0, 5.8, 6.6, 6.6). The upper half has 4 values, so Q3 is the average of the 2nd and 3rd values: $\frac{5.8 + 6.6}{2} = 6.2$.
• Maximum: 6.6.

Step4: Draw the boxplot

• The box goes from Q1 = 2.8 to Q3 = 6.2, with a line at the median = 3.2.
• The left whisker goes from the minimum (2.0) to Q1 (2.8).
• The right whisker goes from Q3 (6.2) to the maximum (6.6).

Answer:

The boxplot should have:

• Minimum: 2.0
• Q1: 2.8
• Median: 3.2
• Q3: 6.2
• Maximum: 6.6

(When drawing, the box is between 2.8 and 6.2, median line at 3.2, left whisker from 2.0 to 2.8, right whisker from 6.2 to 6.6)