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Contemporary Mathematics

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  1. Browse through some news websites to find five stories that report on data and include data visualizations. Can you tell from the report how the data were collected? Was randomization used? Are the visualizations appropriate for the data? Are the visualizations presented in a way that might bias the reader?
  2. We discussed three measures of centrality in this chapter: the mode, the median, and the mean. In a broader context, the mean as we discussed it is more properly called the arithmetic mean, to distinguish it from other types of means. Examples of these include the geometric mean, harmonic mean, truncated mean, and weighted mean. How are these computed? How do they compare to the arithmetic mean? In what situations would each of these be preferred to the arithmetic mean?
  3. Simpson’s Paradox is a statistical phenomenon that can sometimes appear when we observe a relationship within several subgroups of a population, but when the data for all thegroups are analyzed all together, the opposite relationship appears. Find some examples of Simpson’s Paradox in real-world situations, and write a paragraph or two that would explain the concept to someone who had never studied statistics before.
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