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BUS 308 Statistics for Managers

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    Running Head: What I ’ve learned a bout Statistics Debra Johnson What I ’ve learned about Statistics BUS 308 Statistics for Managers Instructor: Travis Hayes February 18, 2025 Reflecting on your experience in the course "Statistics for Managers," what key concepts or techniques have you learned about descriptive statistics, particularly in relation to measures of central tendency? Discuss the importance of these concepts in decision - making and their application in real - world business contexts. In your response, include examples of how these statistical methods can be used to analyze data effectively. Your answer should be between 600 - 800 words .

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    What I ’ve learned ab out Statistics Page 2 Introduction The process of data analysis is that of turning data into significant information. While there are no hard and fast distinctions for analyzing statistical data, ensuring that you have a methodical app roach is vital to an accurate analysis . Transforming data into statistical information and then communicating it accurately is a crucial dynamic of effective decision making. O nce a policy has been implemented , it is necessary to monitor and evaluate the effectiveness of that policy. As Othman (2005) states, ‘Good statistics, therefore, represent a key role in good policy making. ” The impact of policy can be measured with good statistics. I. Descriptive S tatistics In the single factor tests and analysis we have a limitation to choose only one factor for comparison which often fails . I n reality , more than one factor may influence the outcome and comparison of phenomena by in cluding all those factors in a model giving an accurate degree of comparison. Multiple regression is one such technique in which we can include control variables , and as many as possible. We can test the impact of their inclusion, and there is a chance of eliminating the non - significant variables to fit the accurate model. (Hoffmann, 1981). A. Measures of C entr a l T endency . We start thinking about how we can represent a set of numbers with one number that somehow represents the "center". We can then talk about the differences between populations, samples, parameters and statistics. A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are sometimes called measures of central location. They are also classed as summary statistics. The mean (often called

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    What I ’ve learned ab out Statistics Page 3 the average) is most likely the meas ure of central tendency that we are most familiar with, but there are others, such as the median and the mode. (Lund & Lund, 2013) . The mean, median and mode are all valid measures of central tendency, but under different conditions, some measures of central tendency become more appropriate to use than others. In the following sections, we will look at the mean, mode and median, and learn how to calculate them and under what conditions they are most appropriate to be used. (Lund & Lund, 2013) . The Mean (Arithmetic) . The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data . The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. I f we have n values in a data set and they have values x1, x2, ..., xn, the sample mean, usually denoted by (pronounced x bar), is: (Lund & Lund, 2013). This formula is usually written in a slightly different manner using the Greek capitol letter , pronounced "sigma", which means "sum of... ” (Lund & Lund, 2013). I n statistics, samples and populations have very different meanings and these differences are very important, even if, in the case of the mean, they are calculated in the same way. To calculate the population mea n and not the sample mean; use the Greek lower case letter "mu", denoted as μ: (Lund & Lund, 2013). The mea n is essentially a model of the data set. It is the value that is most common. T he mean is not often one of the actual values observed in a data set. O ne of its important properties

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    What I ’ve learned ab out Statistics Page 4 is that it minimizes error in the pre diction of any one value in a data set. That is, it is the value that produces the lowest amount of error from all other values in the data set An important property of the mean is that it includes every value in a data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero. (Lund & Lund, 2013). The Median . We usually prefer the m edian over the mean (or mode) when our data is skewed (i.e., the frequency distribution for our data is skewed). If we consider the normal distribution - as this is the most frequently assessed in statistics - when the data is perfectly normal, the mean, median and mode are identical. T hey all represent the most typical value in the data set. But a s the data becomes skewed the mean loses its ability to provide the best central location for the data because the skewed data is dragging it away from the typical value. However, the median best retains this position and is not as strongly influenced by the skewed values. (Lund & Lund, 2013). The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data. In order to calculate the median, suppose we have the data below: 65 55 89 56 35 14 56 55 87 45 92 We first need to rearrange that data into order of magnitude (smallest first): 14 35 45 55 55 56 56 65 87 89 92 (Lund & Lund, 2013). Our median mark is the middle mark - in this case, 56. It is the middle mark because there are 5 scores before it and 5 scores after it. This works fine when you have an odd number of scores, but what happens when you have an even number of scores? What if you had only 10

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