Table of contents
- 1. Intro to Stats and Collecting Data24m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically53m
- 4. Probability1h 29m
- 5. Binomial Distribution & Discrete Random Variables1h 16m
- 6. Normal Distribution and Continuous Random Variables58m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 5m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
3. Describing Data Numerically
Mean
Problem 6.CRE.1
Textbook Question
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
a. Find the mean xbar.

1
Step 1: Understand the concept of the mean (x̄). The mean is the average of a set of numbers, calculated by summing all the values and dividing by the total number of values.
Step 2: Write down the formula for the mean: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xÌ„</mi><mo>=</mo><mfrac><mrow><mo>∑</mo><mi>x</mi></mrow><mi>n</mi></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∑</mo><mi>x</mi></math> represents the sum of all data points and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is the number of data points.
Step 3: Add up all the wait times provided in the data set: 35 + 35 + 20 + 50 + 95 + 75 + 45 + 50 + 30 + 35 + 30 + 30.
Step 4: Count the total number of data points in the set. In this case, there are 12 wait times.
Step 5: Divide the sum of the wait times by the total number of data points to calculate the mean: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xÌ„</mi><mo>=</mo><mfrac><mrow><mo>∑</mo><mi>x</mi></mrow><mi>n</mi></mfrac></math>.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mean
The mean, often referred to as the average, is a measure of central tendency that is calculated by summing all the values in a data set and then dividing by the number of values. It provides a single value that represents the center of the data distribution, making it useful for understanding the overall trend. In the context of wait times, the mean gives an indication of the typical wait time experienced by visitors.
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Data Set
A data set is a collection of related values or observations that can be analyzed to extract meaningful information. In this case, the wait times for the Tower of Terror ride represent a specific data set. Understanding the structure and context of the data set is crucial for performing statistical calculations, such as finding the mean.
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Central Tendency
Central tendency refers to statistical measures that describe the center or typical value of a data set. The mean, median, and mode are all measures of central tendency, each providing different insights into the data. Recognizing these measures helps in interpreting data effectively, especially when comparing different sets of wait times or understanding variability.
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