MTH 154 Activity 6.

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Feb 20, 2024

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Name: Mean Versus Median 1) Sarah and Andrew were comparing prices of their favorite energy bar. Eight grocery stores sell the PR energy bar for the following prices: $1.09 $1.29 $1.29 $1.35 $1.39 $1.49 $1.59 $1.79 Sarah claims the average price of the candy bar is $1.37 but Andrew disagreed and said the average price of the energy bar is actually $1.41. How did Sarah and Andrew come up with these prices? Based on their calculations, who do you think is correct and why? Andrew based his conclusion on the average by finding the mean of the data. He did so by adding all the prices up and dividing them by the number of bars they had. Sarah found the average by using the median of the prices. Andrew’s method is correct in this scenario because we should use the mean to find the average. 2) Ms. Smith, a math teacher, recently gave a mathematics quiz in her class. The ten quiz scores were: 89 87 93 90 12 91 88 87 83 91 a) Based on the test scores above, would you say the class did well? Why or why not? Based on the test scores, the class did well because only one of them failed. b) If you were Ms. Smith, which average would you use to describe the data: mean, median, or mode? If I was Ms. Smith, I would use the median to find the average because the data has an outlier.

3) Suppose that five graduating seniors on a college basketball team receive the following first- year contract offers to play in the National Basketball Association (zero indicates that the player did not receive a contract offer): 0 0 0 0 $10,000,000 The college claimed that the average senior on this basketball team received a $2 million contract offer. a) Explain how the college came up with this number and why this statement may be misleading. The college used the mean to come up with this number. This statement could be misleading because there is an outlier which skews the average. b) Would another measure of central tendency be a better representative of the data? Support your answer. The mode is the best way to represent this data because the numbers are reoccurring other than the outlier.

Analysis 1) As with the Part I Activity, determine which “average” would be a better fit for the data given. Notice that the first two scenarios are very similar to those done in the activity. Given a dataset, calculate and determine whether the mean or median would be a better representation of the data. As you work through these two problems, be sure to calculate BOTH the mean and median. Be careful in how you choose which “average” to use since the question asks for a particular value. Scenario Mean Median Explanation a) A retail store had total sales of $436, $650, $530, $500, $650, $489, and $423 last week. Which measure of data would make the store’s sales last week appear the most profitable? $525 $500 Using the mean would make the data appear to be the most profitable because the value is higher than the median. b) Suppose you have opened some Nutty Bars to check the company’s claim of an “average” of 8 peanuts per bar. Here is what you found after opening 10 bars: 5, 8, 8, 8, 11, 7, 8, 6, 6, and 6. Which average should the company use to support their claim? 7.3 7.5 They should use the median because it’s closer to their claim of 8, but it’s still not their claim. For a better support to their claim, they should use the mode which equals 8.

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2) For the second part of this activity, determine which “average” would be a better representation WITHOUT being given a specific data set. This will require you to think about WHO is requesting or wants the data and then determine which “average” would better suit their needs. In real-life settings, most companies like to portray themselves in a better “light,” so you will have to think critically about how best to do that. Try to think of all the possibilities that can occur and if you need to, “create” a data set to help you determine which “average” to choose. Scenario Explanation a) The average number of pieces of lost luggage per flight from an airline company’s perspective An airline company would want the lowest number of pieces of luggage lost per flight, so the mode would be the best method. This is because most people keep their luggage meaning the mode would be 0. b) The average weight of potatoes in a 10- pound bag The mean would be the best method to use in this scenario because all the potatoes are most likely roughly the same weight, and we already know how much the entire bag weighs. c) The average age at first marriage for men in America The median would be the best method for this scenario because there is likely to be a large difference in the highest and lowest ages.

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