app1 - 1 APPENDIX 1 2 Figure A1.1: Normal Distribution...

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A1.1 1 APPENDIX 1 BASIC STATISTICS The problem that we face in financial analysis today is not having too little information but too much. Making sense of large and often contradictory information is part of what we are called on to do when analyzing companies. Basic statistics can make this job easier. In this appendix, we consider the most fundamental tools available in data analysis. Summarizing Data Large amounts of data are often compressed into more easily assimilated summaries, which provide the user with a sense of the content, without overwhelming him or her with too many numbers. There a number of ways data can be presented. We will consider two here—one is to present the data in a distribution, and the other is to provide summary statistics that capture key aspects of the data. Data Distributions When presented with thousands of pieces of information, you can break the numbers down into individual values (or ranges of values) and indicate the number of individual data items that take on each value or range of values. This is called a frequency distribution . If the data can only take on specific values, as is the case when we record the number of goals scored in a soccer game, you get a discrete distribution . When the data can take on any value within the range, as is the case with income or market capitalization, it is called a continuous distribution . The advantages of presenting the data in a distribution are twofold. For one thing, you can summarize even the largest data sets into one distribution and get a measure of what values occur most frequently and the range of high and low values. The second is that the distribution can resemble one of the many common ones about which we know a great deal in statistics. Consider, for instance, the distribution that we tend to draw on the most in analysis: the normal distribution, illustrated in Figure A1.1. A1.2 2 Figure A1.1: Normal Distribution A normal distribution is symmetric, has a peak centered around the middle of the distribution, and tails that are not fat and stretch to include infinite positive or negative values. Not all distributions are symmetric, though. Some are weighted towards extreme positive values and are called positively skewed, and some towards extreme negative values and are considered negatively skewed. Figure A1.2 illustrates positively and negatively skewed distributions.
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A1.3 3 Returns Figure A1.2: Skewed Distributions Negatively skewed distribution Positively skewed distribution Summary Statistics The simplest way to measure the key characteristics of a data set is to estimate the summary statistics for the data. For a data series, X 1 , X 2 , X 3 , . . . X n , where n is the number of observations in the series, the most widely used summary statistics are as follows: The mean ( μ) , which is the average of all of the observations in the data series.
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This note was uploaded on 10/06/2011 for the course FIN 413 taught by Professor Irfansafdar during the Summer '11 term at Rochester.

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app1 - 1 APPENDIX 1 2 Figure A1.1: Normal Distribution...

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