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Data organization, estimation, hypothesis testing, propagation of measurement error, error ellipses and bivariate normally distributed data as used in least squares adjustments.
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Upon successful completion, the student will be able to:
Produce histograms and frequency polygons from raw, observed survey data.
Calculate the mean and median of a data set.
Compute the variance and standard deviation of samples of survey measurement.
Use Chebyshev's theorem to illustrate the relationship between the spread of the data and the standard deviation of the data.
Calculate the weighted mean of a data set.
Define the basic laws of probability.
Connect probability to the randomness of error in measurement.
Define discrete probability distributions, their means and variances.
Employ the definition of discrete probability distribution functions to define the binomial distribution.
Define continuous probability functions, their means and variances.
Link the definitions of pdfs to well-defined pdfs such as the normal, student's-t, chi-square and F-distributions.
Use the normal distribution to determine probabilities of observing defined ranges of measurement in survey projects.
Define, intuitively, the Central Limit Theorem.
Use the Central Limit Theorem and knowledge of the normal distribution to develop the ideas of confidence interval estimation.
Estimate confidence intervals for the mean of large and small samples.
Apply confidence interval estimation to engineering and cadastral surveys and the analysis of error in least-square adjustment problems.
Calculate confidence intervals for variances and standard deviations.
Apply variance interval estimation to EDM measurements.
Set up various hypotheses tests.
Recognize type I and type II errors.
Use hypothesis testing in analyzing the outcomes of least square adjustment problems such as determining if the variance factor is satisfactory.
Investigate error propagation in survey calculations.
Calculate propagated in geometric studies such as in triangulation problems.
Apply error propagation to determine the statistical error in a traverse.
Use error propagation as an assist to preliminary investigation in survey design given final design parameters.
Calculate the principal parameters of bivariate data: the correlation coefficient and covariance.
Relate adjustment of observations, variance-covariance matrices and correlation.
Test the correlation coefficient for significance.
Relate the ellipse of error to the bivariate normal distribution.
Link covariance matrices with the ellipse of error.
Use the ellipse of error in analysis of adjustment problems.
Effective as of Fall 2003
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