Modeling Random Samples
from Normal Distributions with OpenOffice Calc & C++
Part I
I shall present some observations on the modeling of taking random
samples from given normal distributions and their approximations of
the general statistical summaries of said normal distributions. The given normal distributions were generated in an OpenOffice Calc
spreadsheet using the function NORMINV(num; mean; stddev). I chose
rand() for num, 100 for mean and standard deviation 34.135 to
generate normal distributions of sizes 1,000, 10,000, and 350,000. I
also chose rand(), a mean of 134.135, and a standard deviation of
34.135 to generate normal distributions of sizes 500, 5,000 and
50,000. All normal distributions were of real valued numbers.
The C++ programs samples and errors read in the normal distributions
which have been generated by OpenOffice and saved in the comma
delimited text .csv format and read them into a standard floating
point value C++ vector. When the given normal distribution had been
read into the vector it is loaded into a custom C++ statistical
calculations class I have implemented and a general statistical
summary report for the entire population is printed at the beginning
of a text file. After this is accomplished random samples from size
2 up to the size of the population of the given normal distribution
are taken and each sample's general statistical summary is added as a
row to a table in the text file, all of which can of course be
compared to the initial general statistical summary of the given
normal distribution considered as an entire population. Below is an
example of a test run of the text file output for a particular run of
./samples 500.csv at the bash terminal command line, or samples
500.csv at the Windows command prompt.
population
n = 500
mean = 101.367
median = 100.863
variance = 1032.66
standard deviation = 32.135
mean deviation = 25.7281
median deviation = 22.2732
skewnewss = -0.10289
median skewness = 0.0470683
random samples
size mean median var std meandev mdndev skw mdnskw
2 108.461 108.461 2996.376 54.739 38.706 38.706 -0.000 0.000
3 97.253 92.826 1545.216 39.309 27.557 32.481 0.111 0.338
4 89.384 87.200 967.988 31.113 25.465 23.281 0.095 0.211
5 111.371 116.794 366.891 19.154 14.484 15.326 -0.105 -0.849
6 99.451 98.133 798.427 28.256 23.507 20.010 0.116 0.140
7 107.015 117.532 2015.066 44.889 33.987 29.466 -0.178 -0.703
8 85.060 94.501 2182.623 46.719 31.297 20.638 -1.102 -0.606
. . .
492 101.266 100.863 1045.855 32.340 25.884 22.710 -0.097 0.037
493 101.477 100.967 1017.018 31.891 25.506 22.102 -0.097 0.048
494 101.216 100.659 1038.744 32.230 25.741 22.283 -0.096 0.052
495 101.336 100.967 1034.720 32.167 25.718 22.268 -0.111 0.034
496 101.572 100.991 1033.031 32.141 25.724 22.381 -0.106 0.054
497 101.343 100.967 1026.704 32.042 25.636 22.268 -0.113 0.035
498 101.290 100.863 1021.343 31.958 25.577 22.188 -0.127 0.040
499 101.314 100.759 1035.407 32.178 25.726 22.259 -0.099 0.052
500 101.367 100.863 1034.730 32.167 25.728 22.273 -0.103 0.047
The
C++ code can be found at:
