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# MATH 4511 - Statistics for Geomatics

## Mathematics Part-time Studies Course

### School of Computing and Academic Studies

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# Course Details

Data organization, estimation, hypothesis testing, propagation of measurement error, error ellipses and bivariate normally distributed data as used in least squares adjustments.

## Credits

4.0

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# Learning Outcomes

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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