Fluent Essays

Help Psychology statisticWhen you were a child, you might have seen a dark brown bottle of a mysterious liquid high on a shelf in your garage, out of your reach. “That’s poison,” a parent might have warned, pointing to the container. “Don’t touch.” It nonetheless had some use. It was there for a reason. This example illustrates a principle: Items that can be misused often have a valid use, and vice versa. An average (e.g. mean, median, and mode) is not an exception; it can be useful, but if it is misused or misinterpreted it can be destructive. In what way might an average be misused? Alternatively, how might an average be misinterpreted? For instance, how can a misinterpreted average pertain to stereotyping? How can we avoid misuse or misinterpretation of averages? Provide a specific example to illustrate your explanation.3-2 Exercise: Measures of Average and Measures of Deviation   Previous  Next  Instructions Using Microsoft Excel, complete the following exercises out of your textbook: · Exercise 14: Perception of Time (Section 4.1: p. 125) 14. Percept ion of Time. The data below are times (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when 1 minute (60 seconds) had passed. What do these data suggest about students’ per-ception of time? 53   52   75   62   68   58   49   49 · Exercise 13: Perception of Time (Section 4.3: p. 145) 13. Percept ion of Time. The following times (in seconds) were recorded when statistics students participated in an experiment to test their ability to determine when 1 minute (60 seconds) had passed: 53   52   75   62   68   58   49   49 In these exercises, you will practice computing measures of average and measures of deviation. Submit both a Word document and two Excel documents as needed to show calculations and interpret the results.4 Describing Data >  4.1 What Is Average? 4.1 What Is Average? The term average is used so often that you may be surprised that it does not always have the same meaning. In this section, well explore common ways of characterizing the center of a data distribution, all of which are sometimes called the “average.” Mean, Median, and Mode Table 4.1 shows the number of movies (original and sequels or prequels) in each of five popular science fiction film franchises. What is the average number of movies in these franchises? One way to answer this question is to compute the mean. (The formal term arithmetic mean is commonly referred to simply as the mean.) We find the mean by dividing the total number of movies by five (because there are five franchises listed in the data set): mean=5+8+13+7+55=385=7.6mean=5+8+13+7+55=385=7.6 mean , equals . fraction 5 plus 8 plus 13 plus 7 plus 5 , over 5 end fraction . equals , 38 over 5 , equals 7.6 We say that these five franchises have a mean of 7.6 movies. More generally, we find the mean of any data set by dividing the sum of all of the data values by the number of data values. The mean is what most people think of as the average. In essence, it represents the balance point for a quantitative data distribution, as shown in Figure 4.1. TABLE 4.1 Five Science Fiction Film Franchises Franchise Number of movies (as of 2016) Alien 5 Planet of the Apes 8 Star Trek 13 Star Wars 7 Terminator 5 Figure 4.1 A histogram made from blocks would balance at the position of its mean. We could also describe the average number of movies by using another measure of center: the median, or middle value, of the data set. To find a median, we first arrange the data values in ascending (or descending) order, repeating data values that appear more than once. The next step depends on whether the number of data values is odd or even. · • Odd: If the number of values is odd, there is exactly one value in the middle of the list, and this value is the median. · • Even: If the number of values is even, there are two values in the middle of the list, and the median is the number that lies halfway between them. For example, arranging the data in Table 4.1 in ascending order, we get 5, 5, 7, 8, 13. There are five data values, which is an odd number. Therefore, the median number of movies among these franchises is 7, because 7 is the middle number in the list. The mode is the most common value or group of values in a data set. In the case of the film franchises, the mode is 5 movies because this value occurs twice in the data set, while the other values occur only once. A data set may have one mode, more than one mode, or no mode. Sometimes the mode refers to a group of closely spaced values rather than a single value. The mode is used more commonly for qualitative data than for quantitative data, because neither the mean nor the median can be used with qualitative data. 4 De