Minded Statistics Mind Map

Mind Map

Recently, we had gone through all the materials covered by AP Statistics. As our teacher announced so far, we students, as separate groups, built mind maps to generalize the entire knowledge system inside the statistics class. I saw a lot of great mind maps from other groups that not only included the necessary things we have to know, but also demonstrated these things with innovative themes, like using some objects to allude to the processes of studying statistics.

The ideals and philosophy behind our groups’ construction were also clear. We separated the learned knowledge into four parts: Collecting Data, Exploring Data, Anticipating Patterns, and Making Inferences, with each part accompanied by certain structure of the plant body, while the plant itself is similar to we students, who are going to make our way to develop understanding about statistics.

The “root” – Collecting Data – is the basis of the entire plant. It is necessary to have good research methods in order to collect, analyze, and use the data we accessed, as root needs to absorb water and minerals from the soil so that the plant can grow taller.

The “stem and leaves” – Exploring Data and Anticipating Patterns – act as support for the plant. We have to harness statistical theories and methods to describe the overall data and predict the trends. Similarly, the stem structurally maintains the plant’s overall shape, where as leaves are required to make nutrients (sugars) through photosynthesis and transport them to the whole organism.

The “flower” – Making Inferences – could be regarded as a beautiful illustration of the plant’s characteristics. We need to infer from the accessed data to get evidence so that we could make conclusions. Like the determinate growth pattern of the apical meristem to floral part should be triggered by biochemical signals and environmental stimuli.

In fact, the plant we drew is a pea plant. It was used by Mendel to conduct research about genetics. Mendel utilized a series of statistical methods, like direct control of the variables, measuring the traits of pea plants, anticipating the probability of phenotypes, and checking his hypothesis using goodness-of-fit test. It was such these statistical methods that aided his generalization of the laws of inheritance. This event, on the other hand, enlightened us to sensibly harness our understanding of statistics and thus make contribution to the development of science, technology and society.

Hope all of you could finally get the “fruits” from statistics!

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Aside

Statistics Q&A

A research paper believes that the use of 2.4 oz. as the average size of a burger sold at McDonald’s is “conservative,” which would result in the estimate of 992.25 million pounds of saturated fat being lower than the actual amount that would be consumed. Explain why the author’s belief might be justified.

Answer:

       This paper conservatively (given progressively larger hamburger sizes) projected that the next 100 billion hamburger patties sold by McDonald’s would be a 2.4-oz. which is the average of the 3.2-ounce Big Mac and the 1.6-ounce hamburger patties. However, there could be some extraneous factors that, due to statistics from different agencies, influence the result. One factor is that the Big Mac was the smallest of the larger burgers that had been sold during McDonald’s most sales-intensive years since the 1980s, indicating that there might be some more heavy burgers that could influence the average weight. On the other hand, according to a survey of a 10% sample of Atlanta-area McDonald’s, the Big Mac now dominates burger sales, and it is reported to be the top seller worldwide. This survey shows us the huge impact of the Big Mac on the overall weight. Moreover, the research concerns about hamburgers’ health effects and their corresponding nutrition facts including saturated fats, so changes in the number of different kinds of burgers being sold could alter researchers’ results.

Do you think it would be possible to collect data that could lead to a value for the average burger size that would be better than 2.4 oz.? If so, explain how you would recommend collecting such data. If not, explain why you think it is not possible.

Answer:

       Although it is commonly believed worldwide that McDonald’s top sale burger is Big Mac, we cannot ensure how much more extent does its sale superior than those of other burgers. Besides, McDonald’s burgers vary in weights and categories significantly, and the numbers of consumers are not the same in different nations either. For instance, Chinese McDonald’s top sale burger is not Big Mac, and China might contain some distinctive small size burgers which could not be brought from other places. Moreover, the burgers that are designed for a specific place(in this example, China) might receive more popularity than other burgers since these burgers are created to meet the favor of local people(Chinese). The above are some confounding variables that lead to confusion. We cannot keep track of the differences in various nations and get plausible value for the average burger size better than 2.4 oz if we could not solve the problems mentioned above correctly. Since these problems are extremely hard to be excluded without the help of McDonald’s, we might conclude that we could not collect the accurate data.