Ferman Claudia MTH 154 Activity 6 PDF

Preview

Summary

This has the answers to a MTH 154 assignment....

Description

Name: Claudia Ferman 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?

Mean= 1.41 Median= 1.37 Mode= 1.29 Sarah used the median method Andrew used the mean method Andrew is correct because you want to use the overall average between all energy bars prices because they are using a smaller pool of samples it will represent the best data. The major outliers aren’t far off from the average value so there are no extremes that will majorly impact the outcome. 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? The class did well because every grade except one was above 83.

b) If you were Ms. Smith, which average would you use to describe the data: mean, median, or mode? I would use the median method because the score of 12 would drastically change the mean value. The median method would give you the most accurate data as to how the class did.

3) Suppose that five graduating seniors on a college basketball team receive the following firstyear 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 came up with this number using the mean method. This method is misleading in this situation because 80% of the players received no contract.

b) Would another measure of central tendency be a better representative of the data? Support your answer.

The median method would be the best because the one contract is a major outlier that will affect the mean. It only represents 20% of the data. The other 80% shows no contracts given.

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 $525 $500 The mean value would make the a) A retail store had total sales of $436, stores sales seem most profitable $650, $530, $500, $650, $489, and $423 because it is a higher number. last week. Which measure of data would make the store’s sales last week appear the most profitable?

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

8

They should use the median value to support their claim because it matches their claim.

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 a) The average number of pieces of lost luggage per flight from an airline company’s perspective

b) The average weight of potatoes in a 10- pound bag

c) The average age at first marriage for men in America

Mean Median

Explanation In this scenario a company should have protocols in place to ensure that luggage isn’t lost. That being the case for the most part the data should be the same. But there might be outlier data points from rare situations that will greatly affect a mean value. So, the median method should be used in order for those outlier data points to not affect the data. In this scenario the mean value would be the best method. This is because the density of a potato is uniform across all potatoes. That means that only the volume or size of a potato will make a difference in the weight. But in a 101pound bag the total volume of all potatoes would remain about the same. So, the only thing that would change is the total number of potatoes that would be needed to fill said bag. The mean method takes total number into better account. The best method for this would be the median method. This is because there is probable a 10 year gap in which most men will marry for the first time, there will be outlier data points that would greatly affect the mean value depending on the sample pool....