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Ch. 5 - Discrete Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 5 - Discrete Probability DistributionsProblem 5.CRE.1ab
Chapter 5, Problem 5.CRE.1ab

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.


0 0 1 2 17 28 21 8


a. Find the mean.
b. Find the median.

Verified step by step guidance
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Step 1: To find the mean, first sum up all the numbers of moons listed: 0, 0, 1, 2, 17, 28, 21, and 8. Use the formula for the mean: \( \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \).
Step 2: Count the total number of planets listed (values provided). This will be the denominator in the mean calculation.
Step 3: For the median, arrange the numbers of moons in ascending order: 0, 0, 1, 2, 8, 17, 21, 28. The median is the middle value when the data set is ordered. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.
Step 4: Identify the two middle values in the ordered list (since there are 8 values, an even number). Add these two middle values together and divide by 2 to calculate the median.
Step 5: Ensure all results are expressed with appropriate units (moons) for both the mean and the median.

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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 then dividing by the number of values. In this context, to find the mean number of moons, you would add the total number of moons for all the planets listed and divide by the number of planets. This measure provides a central value that represents the dataset.
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Median

The median is the middle value in a dataset when the numbers are arranged in ascending order. If there is an even number of observations, the median is the average of the two middle numbers. For the moons of the planets, you would first sort the numbers and then identify the median to understand the central tendency of the dataset.
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Data Representation

Data representation involves organizing and displaying data in a way that makes it easy to analyze and interpret. In this question, the number of moons is represented as a list, which allows for straightforward calculations of statistical measures like the mean and median. Understanding how to represent and manipulate data is crucial for effective statistical analysis.
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Related Practice
Textbook Question

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.


0 0 1 2 17 28 21 8


c. Find the mode.

d. Find the range.

Textbook Question

Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.


c. If you play this game once every day, find the probability of no wins in 365 days.

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Textbook Question

Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.


b. If you play this game once every day, find the mean number of wins in years with exactly 365 days.

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Textbook Question

Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.



c. If two different challenges are randomly selected without replacement, find the probability that they both resulted in an overturned call.

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Textbook Question

Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.



a. If 1 of the 945 challenges is randomly selected, what is the probability that it resulted in an overturned call?

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Textbook Question

Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.



b. If one of the overturned calls is randomly selected, what is the probability that the challenge was made by a woman?

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