USES AND ABUSES Statistics in the Real World 114 CHAPTER 2 Descriptive Statistics EXERCISES 1. Use the Internet or some other resource to find an example of a graph that might lead to incorrect conclusions. 2. You are publishing an article that discusses how drinking red wine can help prevent heart disease. Because drinking red wine might help people at risk for heart disease, you include a graph that exaggerates the effects of drinking red wine and preventing heart disease. Do you think it is ethical to publish this graph? Explain. Uses Descriptive statistics help you see trends or patterns in a set of raw data. A good description of a data set consists of (1) a measure of the center of the data, (2) a measure of the variability (or spread) of the data, and (3) the shape (or distribution) of the data. When you read reports, news items, or advertisements prepared by other people, you are rarely given the raw data used for a study. Instead, you see graphs, measures of central tendency, and measures of variability. To be a discerning reader, you need to understand the terms and techniques of descriptive statistics. Abuses Knowing how statistics are calculated can help you analyze questionable statistics. For instance, you are interviewing for a sales position and the company reports that the average yearly commission earned by the five people in its sales force is $60,000. This is a misleading statement if it is based on four commissions of $25,000 and one of $200,000. The median would more accurately describe the yearly commission, but the company used the mean because it is a greater amount. Statistical graphs can also be misleading. Compare the two time series charts at the left, which show the net profits for the Procter & Gamble Corporation from 2011 through 2020. The data are the same for each chart. The first time series chart, however, has a cropped vertical axis, which makes it appear that the net profit decreased greatly from 2011 to 2012 and from 2014 to 2016, and increased greatly from 2012 to 2014 and from 2016 to 2020. In the second time series chart, the scale on the vertical axis begins at zero. This time series chart correctly shows that the net profit changed modestly during this time period and has been steadily increasing in recent years. (Source: Procter & Gamble Corporation) Ethics Mark Twain helped popularize the saying, “There are three kinds of lies: lies, damned lies, and statistics.” In short, even the most accurate statistics can be used to support studies or statements that are incorrect. Unscrupulous people can use misleading statistics to “prove” their point. Being informed about how statistics are calculated and questioning the data are ways to avoid being misled. Year Net profit (in billions of dollars) Procter & Gamble’s Net Profit 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 Year Net profit (in billions of dollars) Procter & Gamble’s Net Profit 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2 4 6 8 10 12 14
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