FITTING EXAMINATION MARKS TO A GAUSSIAN DISTRIBUTION Program: GaussianFit Data title: Test Data for FitToGaussian - One Data read from input file: GaussDataOne.txt Program executed at 09:03:09 on 08-Dec-2010 Number of students: 100 Number of students present: 99 Number of students absent: 1 Statistic Entered Probability Non-linear marks plot regression mean / mu 60.03 60.03 61.93 standard deviation / sigma 15.08 14.94 17.09 moment skewness -0.28 median skewness 0.01 quartile skewness -0.0 excess kurtosis -0.61 PROBABILITY PLOT ANALYSIS Correlation coefficient: R = 0.98 R squared = 0.96 Sum of squares of the residuals: 399.47 Value Error Coefficient of variation (%) Gradient 1.0 0.01 1.37 Intercept -2.69E-7 0.85 3.16E8 Best Error Coefficient of t-value p-value Estimate variation (%) t P > |t| mu 60.03 0.2 0.34 294.33 0.0 sigma 14.94 0.21 1.37 72.89 0.0 Ordered data Gaussian order Residuals Ordered data Gaussian order Residuals Ordered data Gaussian order Residuals values statistic values statistic values statistic medians medians medians 24.0 22.73 1.27 27.0 27.84 -0.84 31.0 30.79 0.21 32.0 32.93 -0.93 32.0 34.64 -2.64 32.0 36.08 -4.08 33.0 37.32 -4.32 33.0 38.43 -5.43 37.0 39.44 -2.44 40.0 40.36 -0.36 40.0 41.22 -1.22 41.0 42.02 -1.02 42.0 42.77 -0.77 43.0 43.48 -0.48 45.0 44.16 0.84 45.0 44.81 0.19 46.0 45.43 0.57 46.0 46.02 -0.02 46.0 46.6 -0.6 46.0 47.16 -1.16 46.0 47.7 -1.7 47.0 48.22 -1.22 48.0 48.73 -0.73 49.0 49.23 -0.23 49.0 49.72 -0.72 49.0 50.2 -1.2 50.0 50.67 -0.67 50.0 51.12 -1.12 51.0 51.57 -0.57 53.0 52.02 0.98 53.0 52.46 0.55 53.0 52.89 0.12 54.0 53.31 0.69 55.0 53.73 1.27 55.0 54.15 0.86 56.0 54.56 1.45 56.0 54.96 1.04 56.0 55.37 0.64 57.0 55.76 1.24 57.0 56.16 0.84 57.0 56.56 0.45 58.0 56.95 1.05 58.0 57.34 0.66 58.0 57.73 0.28 59.0 58.11 0.89 59.0 58.5 0.5 60.0 58.88 1.12 60.0 59.26 0.74 60.0 59.65 0.35 60.0 60.03 -0.03 60.0 60.41 -0.41 60.0 60.8 -0.8 61.0 61.18 -0.18 61.0 61.56 -0.56 61.0 61.95 -0.95 62.0 62.34 -0.34 63.0 62.72 0.28 63.0 63.11 -0.11 65.0 63.51 1.5 65.0 63.9 1.1 66.0 64.3 1.7 66.0 64.7 1.3 66.0 65.1 0.9 67.0 65.51 1.5 69.0 65.92 3.08 70.0 66.33 3.67 70.0 66.75 3.25 71.0 67.18 3.83 71.0 67.61 3.39 71.0 68.04 2.96 71.0 68.49 2.51 72.0 68.94 3.06 72.0 69.4 2.6 72.0 69.86 2.14 73.0 70.34 2.66 73.0 70.83 2.17 74.0 71.33 2.67 75.0 71.84 3.16 75.0 72.36 2.64 75.0 72.9 2.1 75.0 73.46 1.54 75.0 74.04 0.96 75.0 74.64 0.37 75.0 75.26 -0.26 76.0 75.9 0.1 76.0 76.58 -0.58 76.0 77.29 -1.29 76.0 78.04 -2.04 77.0 78.84 -1.84 78.0 79.7 -1.7 78.0 80.62 -2.62 79.0 81.63 -2.63 79.0 82.74 -3.74 82.0 83.99 -1.99 84.0 85.42 -1.42 85.0 87.13 -2.13 85.0 89.27 -4.27 86.0 92.22 -6.22 92.0 97.33 -5.33 NON-LINEAR REGRESSION ANALYSIS Linear correlation coefficient: experimental y data versus calculated y data R = 0.69 R squared = 0.47 Coefficient of determination: R = 0.69 R squared = 0.47 Adjusted coefficient of determination: R = 0.67 R squared = 0.44 Coefficient of determination F-ratio: F = 18.57 Coefficient of determination F-ratio probability: P = 3.1E-4 Sum of squares of residuals: 117.22 Degrees of freedom: 20.0 Best Error Coefficient of t-value p-value Estimate variation (%) t P > |t| mu 61.93 2.62 4.22 23.69 4.44E-16 sigma 17.09 2.79 16.31 6.13 5.45E-6 Ao 309.11 41.98 13.58 7.36 4.09E-7 Binned marks Bin width: 2.9565217391304346 Bin Experimental Calculated Residuals centre frequency frequency 25.48 1.0 0.74 0.26 28.44 1.0 1.06 -0.06 31.39 4.0 1.46 2.54 34.35 2.0 1.96 0.04 37.3 1.0 2.56 -1.56 40.26 3.0 3.23 -0.23 43.22 2.0 3.96 -1.96 46.17 8.0 4.72 3.28 49.13 6.0 5.45 0.55 52.09 4.0 6.11 -2.11 55.04 6.0 6.66 -0.66 58.0 8.0 7.03 0.97 60.96 10.0 7.21 2.79 63.91 4.0 7.17 -3.17 66.87 4.0 6.92 -2.92 69.83 7.0 6.49 0.51 72.78 6.0 5.9 0.1 75.74 12.0 5.21 6.79 78.7 4.0 4.46 -0.46 81.65 1.0 3.71 -2.71 84.61 4.0 2.99 1.01 87.57 0.0 2.34 -2.34 90.52 1.0 1.78 -0.78 DATA Examination marks used 58.0 56.0 46.0 79.0 61.0 54.0 61.0 60.0 48.0 72.0 76.0 85.0 40.0 33.0 45.0 85.0 75.0 46.0 56.0 78.0 53.0 63.0 84.0 66.0 42.0 49.0 41.0 71.0 46.0 32.0 77.0 62.0 76.0 76.0 75.0 58.0 47.0 72.0 60.0 50.0 86.0 67.0 32.0 69.0 66.0 60.0 58.0 75.0 82.0 60.0 71.0 65.0 50.0 71.0 51.0 60.0 59.0 55.0 27.0 43.0 78.0 75.0 70.0 40.0 79.0 24.0 32.0 70.0 76.0 37.0 57.0 61.0 57.0 66.0 63.0 49.0 45.0 53.0 60.0 75.0 53.0 73.0 55.0 65.0 59.0 56.0 33.0 31.0 71.0 75.0 74.0 49.0 73.0 46.0 75.0 72.0 92.0 57.0 46.0