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Use and Misuse of Percentages

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In a minimum of 200 words, post to the Discussion Area your response to the following:

Find an example of two of the following types of usage of percentages.

Use of percentages as a fraction. Remember that this type will use the word of to imply multiplication. Explain whether this was an effective way to represent this information within the context of the example you found.
Use of percentages to describe change. In the example you find, determine whether the reported percentage demonstrated absolute or relative change. Show your work. Explain whether this was an effective way to represent this information within the context of the example you found.
Use of percentages for comparison. In the example you find, determine whether the reported percentage demonstrated absolute or relative change. Show your work. Explain whether this was an effective way to represent this information within the context of the example you found.
Now, find an example of two of the following misuses of percentages.

Use of a shifting reference value. In this situation, the base values are changing as differing values of percentages are applied as increases, decreases, or both. Percentage increases, decreases, or both do not have a cumulative effect. Be sure to demonstrate why your example fits this category.
Use of percentage to represent less than nothing. Look for an example where you are seeing a reduction of some percentage greater than 100. Be sure to demonstrate why your example fits this category.
Situation where the average percentage is reported. In general, you can not average percentages. The result isn't representative of what actually has occurred in the situation in question. Be sure to demonstrate why your example fits this category.

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Solution Summary

The uses and misuses of percentages are examined. The solution is answered in 343 words. Examples are provided with five references.

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Use of percentages as a fraction.
The probability of getting a 1 when you roll a fair die is 16.67%. this is more effectively represented as the fraction 1/6 because it is clearer that you would expect to roll the number 1 every 1 out of 6 rolls.

Use of percentages to describe change.
The United States census is a collection of data about people in the United States. It includes data about the population and how it has changed over time. This data can be represented as an annual percentage change (1). The U.S. population increased by approximately 0.8% per year from ...

Solution provided by:
J Pye, MSc
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  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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  • "Hello, thank you for your answer for my probability question. However, I think you interpreted the second and third question differently than was meant, as the assumption still stands that a person still independently ranks the n options first. The probability I am after is the probability that this independently determined ranking then is equal to one of the p fixed rankings. Similarly for the third question, where the x people choose their ranking independently, and then I want the probability that for x people this is equal to one particular ranking. I was wondering if you could help me with this. "
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