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hw1 - MA206 Homework 1 Michael Slagh 02 February 06 Part I...

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MA206 / Homework 1 Michael Slagh 02 February 06 Part I: Univariate Data Analysis: Summary statistics for “Whole Candidate Score”. WCS Mean 6045.527 Standard Error 12.73988 Median 6085 Mode 6178 Standard Deviation 383.6797 Sample Variance 147210.1 Kurtosis 0.185342 Skewness -0.28498 Range 2484 Minimum 4789 Maximum 7273 Sum 5483293 Count 907 The statistics show that the mean WCS is about 6045, with our standard deviation about 384. Because we know that within a model usually about 95% of the scores fall within 2 standard deviations of the mean, it is safe to say that the vast majority of the scores are in the 5200-6800 range, and this is quite true. Because we have so much data to choose from, our standard error is quite low, so we can trust the numbers to a high degree of accuracy. Also, the median data point falls above the mean, so I would assume that there may be a few outliers on the bottom range of the data that are bringing the mean down below the middle score. From the empirical distribution function for the data set, I found that 40.1323% of the WCS are below 6000 and 35.6119% of the WCS are above 6200.
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