Question

6c redraw the boxplot after removing the outlier. adjust the edges and whiskers of the boxplot by dragging them to the correct positions.

Answer:

To solve the problem of redrawing the boxplot after removing the outlier, we follow these steps:

Step 1: Identify the Outlier

First, we need to determine which data point is the outlier. In a boxplot, outliers are typically points that lie outside the range of \( Q1 - 1.5 \times IQR \) to \( Q3 + 1.5 \times IQR \), where \( IQR = Q3 - Q1 \) (interquartile range), \( Q1 \) is the first quartile (25th percentile), and \( Q3 \) is the third quartile (75th percentile). From the given boxplot, we can see that the far - right whisker or a data point (the outlier) is likely at a position that is outside the normal range of the data. Let's assume that the outlier is the data point that is far from the main cluster of the box and whiskers. For example, if the original boxplot has a whisker extending to 10 or 11, and the main data is concentrated between, say, 1 and 6 (just an example based on the axis), the outlier could be at 10 or 11.

Step 2: Determine the New Range after Removing the Outlier

After removing the outlier, we need to find the new minimum, \( Q1 \), median, \( Q3 \), and new maximum of the remaining data. Let's assume that after removing the outlier, the data range is from, for example, 1 to 6 (again, this is based on the axis provided, and we need to look at the original boxplot's elements). The box in a boxplot represents the interquartile range (IQR), with the left edge of the box being \( Q1 \), the line inside the box being the median, and the right edge of the box being \( Q3 \). The whiskers extend from the box to the minimum and maximum values of the non - outlier data.

Step 3: Adjust the Boxplot Elements

• Minimum (Left Whisker): Drag the left whisker to the minimum value of the data without the outlier. If the minimum of the remaining data is 1 (from the axis), we set the left whisker at 1.
• \( Q1 \) (Left Box Edge): The left edge of the box (representing \( Q1 \)) should be set to the first quartile of the remaining data. If from the original box (before removing the outlier) the left part of the box was at 3, and after removing the outlier, the \( Q1 \) is still 3 (assuming the outlier was on the right), we keep the left box edge at 3.
• Median (Line in Box): The median line inside the box should be adjusted if the outlier affected the median. But if the outlier was on the right and the median of the remaining data is still, say, 4, we keep the median line at 4.
• \( Q3 \) (Right Box Edge): The right edge of the box (representing \( Q3 \)) should be set to the third quartile of the remaining data. If before removing the outlier the right box edge was at 6, and after removing the outlier (which was on the right), the \( Q3 \) is still 6, we keep the right box edge at 6.
• Maximum (Right Whisker): Drag the right whisker to the maximum value of the data without the outlier. If the maximum of the remaining data is 6 (instead of the outlier's value like 10), we set the right whisker at 6.

Since this is a drag - and - drop type of problem to adjust the boxplot, the final answer would be the boxplot with the left whisker at the new minimum, the box edges at the new \( Q1 \) and \( Q3 \), the median line at the new median, and the right whisker at the new maximum after removing the outlier. (Note: The specific values depend on the actual data set, but the process is as described above to adjust the boxplot elements to reflect the data without the outlier.)

If we assume the outlier was at 10 and the remaining data has min = 1, \( Q1 = 3 \), median = 4, \( Q3 = 6 \), max = 6, the boxplot would have:

• Left whisker at 1.
• Left box edge at 3.
• Median line at 4.
• Right box edge at 6.
• Right whisker at 6.