Ch. 3 - Describing, Exploring, and Comparing Data

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 3 - Describing, Exploring, and Comparing Data

Problem 3.1.24

Chapter 3, Problem 3.1.24

In Exercises 21–24, find the mean and median for each of the two samples, then compare the two sets of results.

It’s a Small Wait After All Listed below are the wait times (minutes) at 10 AM for the rides “It’s a Small World” and “Avatar Flight of Passage.” These data are found in Data Set 33 “Disney World Wait Times.” Does a comparison between the means and medians reveal that there is a difference between the two sets of data?

Verified step by step guidance

Step 1: Organize the data for both samples ('It’s a Small World' and 'Avatar Flight of Passage') into two separate lists. This will help in calculating the mean and median for each dataset.

Step 2: Calculate the mean for each dataset. The mean is computed by summing all the values in the dataset and dividing by the total number of values. Use the formula:

Mean = \frac{\sum x}{n}

, where

x

represents the individual data points and

n

is the total number of data points.

Step 3: Calculate the median for each dataset. To find the median, first sort the data in ascending order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.

Step 4: Compare the mean and median for each dataset. Analyze whether the mean and median are close to each other or if there is a significant difference. This can indicate whether the data is skewed or symmetric.

Step 5: Interpret the comparison between the two datasets. Discuss whether the differences in the means and medians suggest a notable difference in wait times between 'It’s a Small World' and 'Avatar Flight of Passage'. Consider factors such as variability and skewness in the data.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mean

The mean, or average, is calculated by summing all the values in a dataset and dividing by the number of values. It provides a central value that represents the dataset, but it can be influenced by extreme values (outliers). In this context, calculating the mean wait times for both rides will help in understanding the overall experience of visitors.

Median

The median is the middle value of a dataset when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers. The median is a robust measure of central tendency that is less affected by outliers, making it useful for comparing wait times that may have extreme values.

Comparison of Means and Medians

Comparing the means and medians of two datasets can reveal differences in their distributions. If the mean is significantly higher than the median, it may indicate a right-skewed distribution, often due to outliers. In this exercise, analyzing the means and medians of wait times for 'It’s a Small World' and 'Avatar Flight of Passage' will help determine if the wait experiences differ significantly.

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Comparing Mean vs. Median

Related Practice

Textbook Question

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Smart Thermostats Listed below are selling prices (dollars) of smart thermostats tested by Consumer Reports magazine. If you decide to buy one of these smart thermostats, what statistic is most relevant, other than the measures of central tendency?

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

139

views

Textbook Question

In Exercises 21–28, use the same list of cell phone radiation levels given for Exercises 17–20. Find the indicated percentile or quartile.

P30

175

views

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.

Super Bowl Jersey Numbers Listed below are the jersey numbers of the 11 offensive players on the starting roster of the New England Patriots when they won Super Bowl LIII. What do the results tell us?

12 26 46 15 11 87 77 62 60 69 61

299

views

Textbook Question

Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, . . . , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?

0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47

142

views

Textbook Question

Trimmed Mean Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use the axial loads (pounds) of aluminum cans listed below (from Data Set 41 “Aluminum Cans” in Appendix B) for cans that are 0.0111 in. thick. An axial load is the force at which the top of a can collapses. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.

247 260 268 273 276 279 281 283 284 285 286 288

289 291 293 295 296 299 310 504

239

views

Textbook Question

In Exercises 21–28, use the same list of cell phone radiation levels given for Exercises 17–20. Find the indicated percentile or quartile.

P50

130

views