Probability & Statistics

Concepts / Competencies / Assessment / Standards
Introduction to statistics / Identify variables in a statistical study, distinguish between quantitative and
qualitative variables, identify populations and samples, determine the level of
measurement, and compare descriptive and inferential statistics / HW/Quiz / CC.2.4.HS.B.4
Explain the importance of random samples, construct a simple random sample, simulate a random process, and describe different techniques for sampling / HW/Quiz / CC.2.4.HS.B.4
Discuss what it means to take a census, describe simulations, observational studies, and experiments, identify control groups, placebo effects, and random two-treatments, discuss potential pitfalls that might generate unreliable data / HW/Quiz / CC.2.4.HS.B.4
CC.2.4.HS.B.5
Demonstrate knowledge on the statistics introduction / Unit Test
Frequency Distributions & Histrograms / Organize raw data using a frequency table, Construct histograms and relative frequency histograms, Recognize basic distribution shapes, and interpret graphs / HW/Quiz / CC.2.4.HS.B.4
CC.2.4.HS.B.5
Determine types of graphs that are appropriate, construct & interpret bar graphs, pareto charts, circle graphs, and time-series graphs / HW/Quiz / CC.2.4.HS.B.4
CC.2.4.HS.B.5
Construct stem & leaf displays from raw data, use them to visualize data, and compare them to histograms / HW/Quiz / CC.2.4.HS.B.4
CC.2.4.HS.B.5
Demonstrate knowledge on Frequency distributions and histograms / Unit Test
Averages and Variation / Compute & interpret mean, median, and mode, and explain how they are affected by outliers. Calculate trimmed mean and weighted average / HW/Quiz / CC.2.4.HS.B.1
Find the range, variance, standard deviation, coefficient of variation and a Chebyshev interval. Tell why the coefficient of variation is important and also what Chebyshev interval tells us / HW/Quiz / CC.2.4.HS.B.1
Interpret percentiles; compute median, quartiles, five number summaries. Make and interpret box & whisker plots. / HW/Quiz / CC.2.4.HS.B.1
Demonstrate knowledge on averages and variation / Unit Test
Correlation and Regression / Make a scatter diagram, estimate the line of best fit, compute the correlation coefficient r and investigate its meaning / HW/Quiz / CC.2.4.HS.B.2
State the least squares criterion, find & graph the equation of the least squares line and use it to make predictions. Use r2 to determine explained and unexplained variation / HW/Quiz / CC.2.4.HS.B.3
Demonstrate knowledge on correlation and regression / Unit Test
Elementary Probability Theory / Assign probabilities, discuss the law of large numbers, apply basic probability to everyday life, and explain the relationships between statistics & probability / HW/Quiz / CC.2.4.HS.B.6
CC.2.4.HS.B.7
Compute probabilities of compound, independent, and mutually exclusive events. Use surveys to compute conditional probabilities / HW/Quiz / CC.2.4.HS.B.6
CC.2.4.HS.B.7
Organize outcomes in a sample space using tree diagrams. Compute number of outcomes using permutations and combinations. Relate counting techniques to everyday life / HW/Quiz / CC.2.4.HS.B.6
CC.2.4.HS.B.7
Demonstrate knowledge on elementary probability theory / Unit Test
Binomial Distribution / Distinguish between discrete and continuous random variables, graph discrete probability distributions, compute the standard deviation and expected values / HW/Quiz / CC.2.4.HS.B.1
List the features of a binomial experiment, compute binomial probabilities by hand and with a table to solve real-world problems / HW/Quiz / CC.2.4.HS.B.1
Make histograms for binomial distributions / HW/Quiz / CC.2.4.HS.B.1
Demonstrate knowledge of the binomial distribution / Unit Test
Normal Curves and Sampling Distributions / Graph a normal curve and summarize its properties. Apply the empirical rule to solve real-world problems. / HW/Quiz / CC.2.4.HS.B.1
Convert raw data to z scores and vice versa. Graph the standard normal distribution and find areas under the curve / HW/Quiz / CC.2.4.HS.B.1
Compute the probability of standardized events, find z scores from given normal probability, use the inverse normal to solve guarantee problems / HW/Quiz / CC.2.4.HS.B.1
Demonstrate knowledge on Normal Curves and Sampling Distributions Part I / Mid-Unit Test
Review random sample, relative frequency, parameter, statistic, and sampling distribution. Compare relative frequency distributions to theoretical distributions / HW/Quiz / CC.2.4.HS.B.1
Use the expected value and standard deviation to construct theoretical sampling distributions for the sample mean. Learn and explain the central limit theorem / HW/Quiz / CC.2.4.HS.B.1
State the necessary conditions for the normal approximation to the binomial distribution, compute the population mean or expected value and standard deviation for the normal approximation, and convert x values to a range of standardized z scores to find desired probabilities / HW/Quiz / CC.2.4.HS.B.1
Demonstrate knowledge on Normal Curves and Sampling Distributions Part II / Unit Test II
Estimation in Statistics / Explain the meaning of confidence level, estimation error, and critical values. Find the critical value corresponding to a confidence level and compute & interpret confidence intervals for the population when the population mean is known. Compute the sample size for estimating the population mean. / HW/Quiz / CC.2.4.HS.B.5
Compute degrees of freedom and use them along with confidence levels to find critical values and compute intervals for the population mean when the population mean is unknown. / HW/Quiz / CC.2.4.HS.B.5
Compute the margin of error for proportions using confidence levels. Compute confidence intervals for p and interpret the results. Compute the sample size needed to estimate p with or without an estimate for p. / HW/Quiz / CC.2.4.HS.B.5
Demonstrate knowledge for estimation in statistics / Unit Test
Hypothesis Testing / Understand the rationale for statistical tests, identify the null & alternate hypotheses, and identify right, left and two tailed tests. Use a test statistic to calculate a P-value. Recognize errors, level of significance and the power of a test. Understand the meaning and risks of rejecting or not rejecting the null hypothesis. / HW/Quiz / CC.2.4.HS.B.5
Test the population mean when the population standard deviation is known and unknown. Use critical regions or the P-value to test. / HW/Quiz / CC.2.4.HS.B.5
Identify the components needed for testing a proportion, compute a sample test statistic, find the P-value, and conclude the test / HW/Quiz / CC.2.4.HS.B.5
Demonstrate knowledge for hypothesis testing / Unit Test