Exam (elaborations) BMAL 590

What is Statistics? • Descriptive Statistics o A student enrolled in a business undergraduate program is attending his first class of the required business statistics course. The student is somewhat apprehensive because he believes the myth that the course is difficult to pass. To alleviate his anxiety, the student asks the professor about last semester’s student grades. Since the professor is friendly and helpful, like all other statistics professors, he obliges the student and provides a list of the final grades, which are composed of semester or term work plus the final exam. What information can the student obtain from the list? This is a typical statistics problem. The student has the data (grades) and needs to apply statistical techniques to uncover the desired information. This is a function of descriptive statistics. o Descriptive statistics is one of two branches of statistics which focuses on methods of organizing, summarizing, and presenting data in a convenient and informative way. o One form of descriptive statistics uses graphical techniques which allow statistics practitioners to present data in ways that make it easy for the reader to extract useful information. A histogram (or bar graph) can show if the data is evenly distributed across the range of values, if it falls symmetrically from a center peak (normal distribution), if there is a peak but the more of the data falls on one side of the peak than the other (a skewed distribution), or if there are two or more peaks in the data (bi- or multi-modal). Figure 1 shows normal and skewed distributions. o Another form of descriptive statistics uses numerical techniques to summarize data. Rather than providing the raw data, the professor may only share summary data with the student. One such method that you have already used frequently calculates the average or mean. In the same way that a person can calculate the mean age of the employees of a company, the professor can compute the average grade of last semester's course. The actual technique we use depends on what specific information we would like to extract. In this example, we can see several important pieces of information. o The first is the "typical" grade. We call this a measure of central location. The mean (or average) is one such measure; it is the sum of all the data values divided by the number of values. Suppose the student was told that the average grade last year was 67. Is this enough information to reduce his anxiety? The student would likely respond "no" and he would like to know whether most of the grades were close to 67 or if the grades were scattered far below and above the average. He needs a measure of variability. o The simplest such measure is the range, which is calculated by subtracting the smallest number from the largest. Suppose the highest grade is 96 and the lowest grade is 24. The range of grades is 72. .....................................CONTINUED.............