| Examining the Distribution of Final Exam Scores |
| 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 |
| Quantiles (Definition 5) | |||
| Quantile | Estimate | 90% Confidence Limits 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 |
----+----+----+----+
|
Normal Probability Plot
97+ *++
| ++
| *++
| *+++
| ++
| * *+
| +++
| +*
| *+*
| +++
| ++*
| ++
| +*+ *
71+ * ++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
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