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In response, connect students' examples to earlier units of study in this course. For example, point out how a misuse or misinterpretation of an average relates to sampling, ethics, or visual displays.
1st Student Example
When we are looking at determining the average in any study or poll, we have to be careful about our calculations. The average in statistical analysis can have one of three definitions. It can be defined as the mean, median, or mode based off of which of these processes you decide to use. The mean is what most people think of when they think of the word average. The mean is the sum of all the data divided by the number of data present. Say your classes ages are, 21, 22, 28, 28, 32, 36, 40, 46, 51. The mean of this data set would be 33.8. The median for this data set would be 32, and the mode would be 28. Notice how all of these numbers are different, but they are still accurate. This data set doesn’t have a wide variance, nor is it very large, so none of these numbers is too far off from the others. This may not always be the case, though.
When I think of examples of how the average can be misused, I think about the divorce rate. I work with an older generation and that is often a topic of discussion amongst our patients. According to the American Psychological Association, the average divorce rate in America is 40-50%. This statistic was found through the Ace homework tutors - APA website and adapted from the Encyclopedia of Psychology. The question is what criteria are they basing this statistic off of? The most likely answer is they are simply taking the number of all divorces and comparing them to the number of marriages. Yes, this tells us that 40-50% of marriages end in divorce but that doesn’t tell us how many of those marriages happened between teens (18-19), how many of those marriages ended because of addiction, unplanned pregnancy, lack of pregnancy, infidelity, or financial struggles. There are numerous reasons why a marriage might end and only telling us the average percentage of divorce does the topic a disservice. Siting a recent article by Dana Rotz, brides that got married in their 30s held relationships that were 4 times as stable as those of brides that were in their teens when they got married (Rotz, D. 2016: 2024 - Do my homework - Help write my assignment online, p962). Using the average number of divorces without digging deeper to understand why paints a negative picture about marriage. When a young person is considering getting married, they likely don’t want to hear that 50% of all marriages end in divorce. If they use these statistics, their marriage has a 50% chance of being successful. I don’t know about you, but I wouldn’t like those odds.
References
Rotz, D. (2016: 2024 - Do my homework - Help write my assignment online). Why Have Divorce Rates Fallen? Journal of Human Resources, 51(4), 961–1002. https://doi-org.ezproxy.snhu.edu/10.3368/jhr.51.4.0214-6224R
https://www.apa.org/topics/divorce-child-custody
2nd student example
Averages sound like a good idea and can be applied in some situations, but are not always the correct answer for all situations. In the case of the five basketball players where only one received a $100 million contract, the rule of averages would dictate that each student on average receives a $20 million contract, which simply isn’t the case. In other circumstances, averages can be misused or misinterpreted. Advertisers will purposely use averages to promote and sell products. It may say something like, “80% of users agree”. They fail to mention who they are polling and what the demographics in the sample population may be. The percentages can also be skewed, because they are only polling people who want to use the product in the first place.
Alternatively, averages can also be misinterpreted. An example of this could be a story on the nightly news where they discuss how 10% of African Americans are committing violent crimes in some city. This is an example of misinterpretation for many reasons. There could be only 10 African Americans in the city and one committed a violent crime. Plus, there is a focus solely on one cultural group; they fail to mention latinos, hispanics, causasians, asian americans, etc. What if the population is 85% caucasian and they are committing most of the violent crime. If the question was what percentage of violent crime is committed by African Americans in the city, it would be remarkably lower. It’s all about how the data is framed and interpreted. One way to avoid misuse or misinterpretation would be to consider the source of the information and dig a little deeper on the data, as far as where it is from and what are the motives of those who are presenting it. The Eight Guidelines for Critically Evaluating a Statistical Study is a good tool for those who want to interpret the data of averages and studies.
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