Activity 6 - Mean Versus Median

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School

Northern Virginia Community College *

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Course

MAT154

Subject

Economics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by DoctorBeaverMaster328

Problem 1: Sarah and Andrew's Energy Bar Prices a) To determine who is correct between Sarah and Andrew, we need to understand how each of them calculated their averages. Sarah calculated the average price by adding up all the prices and dividing them by the number of prices (8 in this case): (1.09 + 1.29 + 1.29 + 1.35 + 1.39 + 1.49 + 1.59 + 1.79) / 8 = $1.37. Andrew calculated the average price in a similar manner: (1.09 + 1.29 + 1.29 + 1.35 + 1.39 + 1.49 + 1.59 + 1.79) / 8 = $1.41. b) Both Sarah and Andrew calculated the mean (average) price by adding up all the prices and dividing by the number of prices. In this case, both used the same method. c) Since both Sarah and Andrew used the same method to calculate the mean, it's a matter of arithmetic accuracy. Andrew's calculation of $1.41 is correct based on the given data. d) In this scenario, the term "average" refers to the mean, which is the sum of all values divided by the number of values. In statistics, "average" usually means the mean. e) While the price difference between Sarah's and Andrew's calculations is not significant, it can matter in scenarios where precision is essential, especially when dealing with large datasets or making financial decisions. Using the correct average ensures more accurate results. Problem 2: Ms. Smith's Math Quiz Scores a) To determine if the class did well, let's first look at the data overall. It appears that most students scored in the high 80s and low 90s, with one outlier at 12. Based on this observation, we can say that most of the class performed well, but there is a significant outlier that affected the overall average. b) Considering the outlier, it might be better to use the median instead of the mean to describe the data. The median is less affected by outliers. Let's calculate the median:

Arrange the scores in ascending order: 12, 83, 87, 87, 88, 89, 90, 91, 91, 93. Since there are 10 scores (an even number), the median is the average of the two middle values, which are 88 and 89. Median = (88 + 89) / 2 = 177 / 2 = 88.5. So, as Ms. Smith, I would use the median (88.5) to describe the data because it provides a better representation, especially considering the outlier. Problem 3: College Basketball Contract Offers a) The college calculated the average senior's contract offer by summing all the offers and dividing by the number of seniors: (0 + 0 + 0 + 0 + 10,000,000) / 5 = $2,000,000. However, this statement is misleading because the presence of a single very high contract offer ($10,000,000) significantly skews the mean. In reality, four out of five seniors did not receive any offers, and the majority did not receive $2 million offers. b) In this scenario, the median would be a better representative of the data because it is not as affected by extreme values. Let's calculate the median: Arrange the offers in ascending order: 0, 0, 0, 0, 10,000,000. The median is the middle value, which is 0. So, the median offer is $0, which accurately reflects the fact that most seniors did not receive any contract offers.

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