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


Tower of Terror Wait Times


a. Find Q1, Q2 and Q3.

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 median (Q2). The median is the middle value of the ordered data. Since there are 12 data points (even number), the median is the average of the 6th and 7th values in the ordered list. Locate the 6th and 7th values, which are both 35, and calculate their average.
3. Step 3: Find Q1 (the first quartile). Q1 is the median of the lower half of the data (the first 6 values in the ordered list: 20, 30, 30, 30, 35, 35). Identify the middle value of this subset, which is the average of the 3rd and 4th values.
4. Step 4: Find Q3 (the third quartile). Q3 is the median of the upper half of the data (the last 6 values in the ordered list: 35, 45, 50, 50, 75, 95). Identify the middle value of this subset, which is the average of the 3rd and 4th values.
5. Step 5: Summarize the results. Q1, Q2, and Q3 represent the first quartile, median, and third quartile, respectively. These values divide the data into four equal parts, providing insights into the distribution of the wait times.

Key Concepts

Quartiles

Quartiles are values that divide a data set into four equal parts, each containing 25% of the data. 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 measures help summarize the distribution of the data and identify its spread.

Median

The median is the middle value of a data set when it is ordered from least to greatest. If the number of observations is odd, the median is the middle number; if even, it is the average of the two middle numbers. The median is a robust measure of central tendency, less affected by outliers than the mean.

Data Set Ordering

Ordering a data set involves arranging the values in ascending or descending order, which is essential for calculating quartiles and medians. This process allows for a clear understanding of the data's distribution and helps in identifying key statistical measures, such as Q1, Q2, and Q3, which are based on the ordered values.