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unbiased vs. biased estimators
consider the population size of the household of my immediate family members. compute the mean, median, range, standard deviation and caruance of this population.
Math 1342 Project #1: Unbiased vs Biased Estimators In our class, we worked with a population of size "3" and showed that the n-1 computation for variance gave us a figure such that the mean of the variances of all the samples was equal to the variance of the population-sample variance is an unbiased estimator for population variance. Here you will be examining a population of size "5" and examining which of mean, median, range, standard deviation, and variance are unbiased. a) Consider the population of the size of the households of my immediate family members: (1,2,4,4,6); compute the mean, median, range, standard deviation, and variance of this POPULATION. b) Now consider the possible random samples from this population with n= 2 (you should identify 25 such samples). For each of these SAMPLES, compute the mean, median, range, standard deviation, and variance (hint: with n=2, the median is the same as the mean). c) At this point, you should have produced five data sets (four distinct) with 25 data valuc each; find the mean (only the mean) of each of these sets.
d) Compare the mean of the sample statistic data from c) with the population parameters computed in a)- which of these are unbiased estimators? e) Write a brief (1-2 paragraph) summary of your procedure and findings.