On the statistics of Number of Comparisons of Quicksort for lists of length 10000 If you apply Quicksort to a random list of length , 10000 The expected number of comparisons is, 155771.6959 The standard deviation is, 6470.626384 The probability that the number of steps takes less than, 154840., is approx. equal to , 0.0092476 The probability that the number of steps takes less than, 154910., is approx. equal to , 0.019525 The probability that the number of steps takes less than, 154950., is approx. equal to , 0.028639 The probability that the number of steps takes less than, 154990., is approx. equal to , 0.038176 The probability that the number of steps takes less than, 155020., is approx. equal to , 0.049599 The probability that the number of steps takes less than, 155040., is approx. equal to , 0.057389 The probability that the number of steps takes less than, 155070., is approx. equal to , 0.068879 The probability that the number of steps takes less than, 155090., is approx. equal to , 0.078325 The probability that the number of steps takes less than, 155110., is approx. equal to , 0.088470 The probability that the number of steps takes less than, 155140., is approx. equal to , 0.099302 The probability that the number of steps takes less than, 155150., is approx. equal to , 0.10690 The probability that the number of steps takes less than, 155170., is approx. equal to , 0.11883 The probability that the number of steps takes less than, 155190., is approx. equal to , 0.12713 The probability that the number of steps takes less than, 155200., is approx. equal to , 0.13570 The probability that the number of steps takes less than, 155220., is approx. equal to , 0.14904 The probability that the number of steps takes less than, 155240., is approx. equal to , 0.15823 The probability that the number of steps takes less than, 155250., is approx. equal to , 0.16766 The probability that the number of steps takes less than, 155260., is approx. equal to , 0.17731 The probability that the number of steps takes less than, 155280., is approx. equal to , 0.18716 The probability that the number of steps takes less than, 155290., is approx. equal to , 0.19721 The probability that the number of steps takes less than, 155310., is approx. equal to , 0.20744 The probability that the number of steps takes less than, 155320., is approx. equal to , 0.21783 The probability that the number of steps takes less than, 155330., is approx. equal to , 0.22839 The probability that the number of steps takes less than, 155350., is approx. equal to , 0.23908 The probability that the number of steps takes less than, 155360., is approx. equal to , 0.24990 The probability that the number of steps takes less than, 155370., is approx. equal to , 0.25536 The probability that the number of steps takes less than, 155380., is approx. equal to , 0.26635 The probability that the number of steps takes less than, 155400., is approx. equal to , 0.27743 The probability that the number of steps takes less than, 155410., is approx. equal to , 0.28860 The probability that the number of steps takes less than, 155430., is approx. equal to , 0.29984 The probability that the number of steps takes less than, 155430., is approx. equal to , 0.30549 The probability that the number of steps takes less than, 155450., is approx. equal to , 0.31681 The probability that the number of steps takes less than, 155460., is approx. equal to , 0.32817 The probability that the number of steps takes less than, 155480., is approx. equal to , 0.33956 The probability that the number of steps takes less than, 155480., is approx. equal to , 0.34526 The probability that the number of steps takes less than, 155500., is approx. equal to , 0.35667 The probability that the number of steps takes less than, 155510., is approx. equal to , 0.36808 The probability that the number of steps takes less than, 155530., is approx. equal to , 0.37948 The probability that the number of steps takes less than, 155530., is approx. equal to , 0.38518 The probability that the number of steps takes less than, 155550., is approx. equal to , 0.39654 The probability that the number of steps takes less than, 155560., is approx. equal to , 0.40788 The probability that the number of steps takes less than, 155580., is approx. equal to , 0.41917 The probability that the number of steps takes less than, 155580., is approx. equal to , 0.42480 The probability that the number of steps takes less than, 155600., is approx. equal to , 0.43601 The probability that the number of steps takes less than, 155610., is approx. equal to , 0.44716 The probability that the number of steps takes less than, 155630., is approx. equal to , 0.45824 The probability that the number of steps takes less than, 155640., is approx. equal to , 0.46925 The probability that the number of steps takes less than, 155650., is approx. equal to , 0.47472 The probability that the number of steps takes less than, 155660., is approx. equal to , 0.48559 The probability that the number of steps takes less than, 155680., is approx. equal to , 0.49638 The probability that the number of steps takes less than, 155690., is approx. equal to , 0.50706 The probability that the number of steps takes less than, 155700., is approx. equal to , 0.51765 The probability that the number of steps takes less than, 155720., is approx. equal to , 0.52812 The probability that the number of steps takes less than, 155730., is approx. equal to , 0.53848 The probability that the number of steps takes less than, 155750., is approx. equal to , 0.54873 The probability that the number of steps takes less than, 155760., is approx. equal to , 0.55885 The probability that the number of steps takes less than, 155780., is approx. equal to , 0.56885 The probability that the number of steps takes less than, 155790., is approx. equal to , 0.57872 The probability that the number of steps takes less than, 155800., is approx. equal to , 0.58847 The probability that the number of steps takes less than, 155820., is approx. equal to , 0.59808 The probability that the number of steps takes less than, 155830., is approx. equal to , 0.60755 The probability that the number of steps takes less than, 155850., is approx. equal to , 0.61689 The probability that the number of steps takes less than, 155860., is approx. equal to , 0.62608 The probability that the number of steps takes less than, 155880., is approx. equal to , 0.63961 The probability that the number of steps takes less than, 155900., is approx. equal to , 0.64845 The probability that the number of steps takes less than, 155910., is approx. equal to , 0.65715 The probability that the number of steps takes less than, 155930., is approx. equal to , 0.66992 The probability that the number of steps takes less than, 155950., is approx. equal to , 0.67826 The probability that the number of steps takes less than, 155960., is approx. equal to , 0.68644 The probability that the number of steps takes less than, 155980., is approx. equal to , 0.69844 The probability that the number of steps takes less than, 156000., is approx. equal to , 0.70626 The probability that the number of steps takes less than, 156020., is approx. equal to , 0.71771 The probability that the number of steps takes less than, 156040., is approx. equal to , 0.72883 The probability that the number of steps takes less than, 156060., is approx. equal to , 0.73962 The probability that the number of steps takes less than, 156070., is approx. equal to , 0.74663 The probability that the number of steps takes less than, 156090., is approx. equal to , 0.75688 The probability that the number of steps takes less than, 156120., is approx. equal to , 0.76680 The probability that the number of steps takes less than, 156140., is approx. equal to , 0.77954 The probability that the number of steps takes less than, 156170., is approx. equal to , 0.78873 The probability that the number of steps takes less than, 156190., is approx. equal to , 0.79762 The probability that the number of steps takes less than, 156220., is approx. equal to , 0.80899 The probability that the number of steps takes less than, 156240., is approx. equal to , 0.81984 The probability that the number of steps takes less than, 156270., is approx. equal to , 0.82764 The probability that the number of steps takes less than, 156290., is approx. equal to , 0.83760 The probability that the number of steps takes less than, 156330., is approx. equal to , 0.84937 The probability that the number of steps takes less than, 156360., is approx. equal to , 0.85827 The probability that the number of steps takes less than, 156390., is approx. equal to , 0.86875 The probability that the number of steps takes less than, 156430., is approx. equal to , 0.87856 The probability that the number of steps takes less than, 156470., is approx. equal to , 0.88949 The probability that the number of steps takes less than, 156510., is approx. equal to , 0.89956 The probability that the number of steps takes less than, 156560., is approx. equal to , 0.90881 The probability that the number of steps takes less than, 156610., is approx. equal to , 0.91996 The probability that the number of steps takes less than, 156670., is approx. equal to , 0.92989 The probability that the number of steps takes less than, 156730., is approx. equal to , 0.93972 The probability that the number of steps takes less than, 156810., is approx. equal to , 0.94916 The probability that the number of steps takes less than, 156900., is approx. equal to , 0.95943 The probability that the number of steps takes less than, 157020., is approx. equal to , 0.96998 The probability that the number of steps takes less than, 157170., is approx. equal to , 0.97987 The probability that the number of steps takes less than, 157440., is approx. equal to , 0.98995 --------------------- This took, 0.355, seconds.