In Exercises 1 and 2, use the following wait times (minutes) at 10:00 AM for the Tower of Terror ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B).


35 35 20 50 95 75 45 50 30 35 30 30


b. Construct a boxplot.

Verified step by step guidance

1. Step 1: Organize the data in ascending order. The given wait times are: 35, 35, 20, 50, 95, 75, 45, 50, 30, 35, 30, 30. Arrange them in increasing order: 20, 30, 30, 30, 35, 35, 35, 45, 50, 50, 75, 95.
2. Step 2: Identify the five-number summary for the data. These include the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. Use the ordered data to calculate these values.
3. Step 3: Calculate Q1 (first quartile) and Q3 (third quartile). Q1 is the median of the lower half of the data (excluding the overall median), and Q3 is the median of the upper half of the data (excluding the overall median).
4. Step 4: Determine the interquartile range (IQR) using the formula: $\mathrm{IQR}=Q_3-Q_1$. Use the IQR to identify any potential outliers, which are values below $Q_1-1.5\times \mathrm{IQR}$ or above $Q_3+1.5\times \mathrm{IQR}$.
5. Step 5: Construct the boxplot. Draw a box from Q1 to Q3 with a line at the median (Q2). Extend whiskers from the box to the minimum and maximum values that are not outliers. Mark any outliers separately as individual points.

Key Concepts

Boxplot

A boxplot, or box-and-whisker plot, is a graphical representation of a dataset that displays its central tendency and variability. It shows the median, quartiles, and potential outliers, providing a visual summary of the distribution. The box represents the interquartile range (IQR), which contains the middle 50% of the data, while the 'whiskers' extend to the smallest and largest values within 1.5 times the IQR from the quartiles.

Quartiles

Quartiles are values that divide a dataset into four equal parts, helping to understand its distribution. The first quartile (Q1) is the median of the lower half of the data, the second quartile (Q2) is the overall median, and the third quartile (Q3) is the median of the upper half. These values are essential for constructing a boxplot, as they determine the box's edges and the whiskers' extent.

Outliers

Outliers are data points that significantly differ from other observations in a dataset. They can skew the results and affect statistical analyses. In the context of a boxplot, outliers are typically identified as points that lie beyond 1.5 times the IQR from the quartiles, and they are often represented as individual dots outside the whiskers, indicating their potential impact on the overall data interpretation.