A Univariate Analysis with Tests for Normality and Plots of the Data Distribution

Examining the Distribution of Final Exam Scores 1 The UNIVARIATE Procedure Variable: Final Moments N 12 Sum Weights 12 Mean 82.4166667 Sum Observations 989 Std Deviation 8.59659905 Variance 73.9015152 Skewness 0.22597472 Kurtosis -1.0846549 Uncorrected SS 82323 Corrected SS 812.916667 Coeff Variation 10.4306561 Std Error Mean 2.48162439 Basic Statistical Measures Location Variability Mean 82.41667 Std Deviation 8.59660 Median 81.50000 Variance 73.90152 Mode 80.00000 Range 26.00000 Interquartile Range 14.50000 Basic Confidence Limits Assuming Normality Parameter Estimate Lower 90% CL Mean 82.41667 79.03314 Std Deviation 8.59660 6.85984 Variance 73.90152 47.05738 Tests for Location: Mu0=80 Test -Statistic- -----p Value------ Student's t t 0.973825 Pr > |t| 0.3511 Sign M 1 Pr >= |M| 0.7539 Signed Rank S 8 Pr >= |S| 0.4434 Tests for Normality Test --Statistic--- ------p Value------ Shapiro-Wilk W 0.952903 Pr < W 0.6797 Kolmogorov-Smirnov D 0.113328 Pr > D >0.1500 Cramer-von Mises W-Sq 0.028104 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.212693 Pr > A-Sq >0.2500

Examining the Distribution of Final Exam Scores 2 The UNIVARIATE Procedure Variable: Final Quantiles (Definition 5) 90% Confidence Limits Quantile Estimate Assuming Normality 100% Max 97.0 99% 97.0 96.30698 114.6289 95% 97.0 91.55028 105.9399 90% 93.0 88.89956 101.4163 75% Q3 89.0 84.12815 94.1623 50% Median 81.5 77.95996 86.8734 25% Q1 74.5 70.67102 80.7052 10% 72.0 63.41705 75.9338 5% 71.0 58.89343 73.2831 1% 71.0 50.20448 68.5264 0% Min 71.0 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 71 5 86 6 72 7 87 1 73 11 91 2 76 12 93 8 80 9 97 3 Stem Leaf # Boxplot 96 0 1 | 94 | 92 0 1 | 90 0 1 | 88 +-----+ 86 00 2 | | 84 | | 82 0 1 | + | 80 00 2 *-----* 78 | | 76 0 1 | | 74 +-----+ 72 00 2 | 70 0 1 | ----+----+----+----+

Examining the Distribution of Final Exam Scores 3 The UNIVARIATE Procedure Variable: Final Normal Probability Plot 97+ *++ | ++ | *++ | *+++ | ++ | * *+ | +++ | +* | *+* | +++ | ++* | ++ | +*+ * 71+ * ++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2