Course Content Summary
Course Prefix and Number -- Course Title
MTH 157: Elementary Statistics (3 cr.)
VCCS Course Description
MTH 157 presents elementary statistical methods and concepts including descriptive statistics,
estimation, hypothesis testing, linear regression, and categorical data analysis. (Credit will not be
awarded for both MTH 157 and MTH 240 or MTH 241.) Lecture 3-4 hours per week.
General Purpose
The general purpose of this one-semester course is to prepare students for study in an applied
science field, such as nursing or police science, that integrates statistical information into the
program content.
Course Prerequisites/Corequisites
MTE 1-5 (two-year shelf life) and ENG 111 eligible
General Education Outcomes
Degree graduates will demonstrate the ability to:
GEO 2.6
GEO 6.1
GEO 6.2
GEO 6.3
GEO 6.4
GEO 6.5
GEO 6.6
Use problem solving skills
Use logical and mathematical reasoning within the context of various disciplines
Interpret and use mathematical formulas
Interpret mathematical models such as graphs, tables, and schematics, and draw
inferences from them
Use graphical, symbolic, and numerical methods to analyze, organize, and
interpret data
Estimate and consider answers to mathematical problems in order to determine
reasonableness
Represent mathematical information numerically, symbolically, and visually using
graphs and charts
Departmental Approval: Spring 2014
Course Outcomes
Upon completing the course, the student will be able to:
A. Appropriately use statistical language.
1. Define “statistics” in two different ways.
2. Describe the basic ideas behind a statistical study.
3. Recognize representative sample and describe its importance.
4. Identify methods of sampling.
5. Explain the differences between observational studies and experiments.
6. Recognize and explain the key issues in experiments, including the selection of
treatment and control groups, the placebo effect, and blinding.
7. Evaluate statistical studies in the media to determine whether the results are
meaningful.
8. Identify data as qualitative or quantitative.
9. Identify quantitative data as discrete or continuous.
10. Assign data a level of measurement.
11. Explain the difference between random and systematic errors, describe errors by
their absolute and relative sizes, and know the difference between accuracy and
precision in measurements.
12. Describe how percentages are used to report statistical results and recognize ways
in which they are sometimes misused.
13. Explain the concept of an index number.
B. Appropriately display and analyze data.
1. Create and interpret frequency tables.
2. Create and interpret basic bar graphs, dotplots, pie charts, histograms, stem-andleaf plots, line charts, and time-series diagrams.
3. Interpret complex graphs used in news media.
4. Critically evaluate graphics and identify common ways in which graphics can be
misleading.
C. Compute measures of statistics.
1. Find the mean, median and mode of a set of data.
2. Describe how each measure of central tendency is affected by outliers.
3. Describe the general shape of a distribution in terms of its number of modes,
skewness, and variation.
4. Interpret common measures of variation: range, five-number summary, and
standard deviation.
D. Apply the concepts of a normal distribution to analyze and describe samples and
populations.
1. Understand normal distribution and identify situations in which normal
distribution is likely to arise.
2. Interpret the normal distribution in terms of the 68-95-99.7 rule, standard scores,
and percentiles.
3. Understand the basic idea behind the Central Limit Theorem and its important
role in statistics.
Departmental Approval: Spring 2014
4. Understand the concept of statistical significance and the essential role that
probability plays in defining it.
E. Solve probability problems.
1. Find probabilities using theoretical and relative frequency methods.
2. Construct basic probability distributions.
3. Use law of large numbers to calculate expected values.
4. Compute and interpret various measures of risk as they apply to travel, disease,
and life expectancy.
F. Determine correlation and causality.
1. Define and interpret correlation.
2. Recognize positive and negative correlations on scatter diagrams.
3. Evaluate the strength of correlation.
4. Recognize best-fit line for a correlation and evaluate the predictive value of such.
G. Estimate population parameters.
1. Explain the fundamental ideas of sampling distributions.
2. Estimate population means and proportions.
3. Compute the margins of error.
4. Construct confidence intervals for population means and proportions.
H. Run hypothesis and t-tests, drawing conclusions from the results.
1. State the null and alternative hypothesis for a hypothesis test.
2. Determine the possible outcomes of a hypothesis test and decide between these
possible outcomes.
3. Interpret one- and two-tailed hypothesis tests for claims made about population
means.
4. Recognize and avoid common errors in hypothesis testing.
5. Interpret hypothesis tests for claims made about population proportions.
6. Appropriately use the Student t distribution for constructing confidence intervals
or conducting hypothesis tests.
Major Topics to be Included
1. Statistical language
2. Descriptive statistics
3. Normal distributions
4. Probability
5. Correlation
6. Estimation
7. Hypothesis testing
Departmental Approval: Spring 2014