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Ch. 3 - Describing, Exploring, and Comparing Data
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 3 - Describing, Exploring, and Comparing DataProblem 3.CQQ.1
Chapter 3, Problem 3.CQQ.1

Mean of Roller Coaster Speeds Listed below are maximum speeds (km/h) of randomly selected roller coasters in the United States. Find the mean.
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1
Step 1: Understand the concept of mean. 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: Add all the maximum speeds together. Use the formula: ∑xi, where xi represents each individual speed value.
Step 3: Count the total number of roller coaster speeds provided. This will be the denominator in the mean formula.
Step 4: Divide the sum of the speeds by the total number of values using the formula: ∑xin, where n is the number of values.
Step 5: Interpret the result as the mean maximum speed of the roller coasters in the dataset.

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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 dataset and then dividing by the number of values. It provides a single value that represents the overall level of the data, making it useful for understanding the general trend. In the context of roller coaster speeds, calculating the mean speed helps to summarize the performance of the selected coasters.
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Calculating the Mean

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 data set consists of the maximum speeds of various roller coasters, which are numerical values that can be used to calculate statistical measures like the mean. Understanding the composition of the data set is crucial for accurate analysis and interpretation.
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Visualizing Qualitative vs. Quantitative Data

Statistical Calculation

Statistical calculations involve mathematical operations applied to data sets to derive insights or summarize information. For finding the mean, the calculation requires adding all the values together and dividing by the count of those values. This process is fundamental in statistics, as it allows for the quantification of data characteristics and aids in making comparisons across different datasets.
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Step 2: Calculate Test Statistic
Related Practice
Textbook Question

Sugar Listed below are measured weights (mg) of sugar in Domino packets labelled as containing 3500 mg (or 3.5 g).


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d. Given that the weights are from Domino sugar packets selected from a much larger population, are the weights a sample or a population?

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Textbook Question

Identifying Significant Values with the Range Rule of Thumb. In Exercises 33–36, use the range rule of thumb to identify the limits separating values that are significantly low or significantly high.


U.S. Presidents Based on Data Set 22 “Presidents” in Appendix B, at the time of their first inauguration, presidents have a mean age of 55.2 years and a standard deviation of 6.9 years. Is the minimum required 35-year age for a president significantly low?

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Textbook Question

Roller Coaster Speed Outlier Identify any outliers among the data listed for Exercise 1.

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Textbook Question

In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.


Smart Thermostats Listed below are selling prices (dollars) of smart thermostats tested by Consumer Reports magazine. Are any of the resulting statistics helpful in selecting a smart thermostat for purchase?



250 170 225 100 250 250 130 200 150 250 170 200 180 250

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Textbook Question

The Empirical Rule Based on Data Set 1 “Body Data” in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells/) Using the empirical rule, what is the approximate percentage of women with platelet counts


a. within 2 standard deviations of the mean, or between 124.3 and 385.9?

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Textbook Question

Normal Distribution Examine the distribution shown in the histogram from Exercise 6. Does it appear that the sample data are from a population with a normal distribution? Why or why not?

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