High School Statistics Curriculum
Below are skills needed, with links to resources to help with that skill. We also encourage plenty of exercises and book work. Curriculum Home
Important: this is a guide only.
Check with your local education authority to find out their requirements.
High School Statistics | Data
Categorize data as qualitative or quantitative
Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions
Identify and describe sources of bias and its effect, drawing conclusions from data
Determine whether the data to be analyzed is univariate or bivariate
Determine when collected data or display of data may be biased
Understand the differences among various kinds of study (e.g., sample, survey, observation, controlled experiment, census)
Determine factors which may affect the outcome of a survey
Categorize quantitative data as discrete or continuous.
High School Statistics | Probability
Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces
Determine the number of elements in a sample space and the number of favorable outcomes
Calculate the probability of an event and its complement
Determine empirical probabilities based on specific sample data
Determine, based on calculated probability of a set of events, if:
* some or all are equally likely to occur
* one is more likely to occur than another
* whether or not an event is certain to happen or not to happen
Calculate the probability of:
* a series of independent events
* two mutually exclusive events
* two events that are not mutually exclusive
Calculate theoretical probabilities, including geometric applications
Calculate empirical probabilities
Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most
Use tree diagrams to aid in the calculation of probabilities
Understand how 'false positives' or 'false negatives' can influence the results of an experiment, and use tree diagrams to work out their probabilities.
Calculations of 'Shared birthday' and related problems in probability.
Compare empirical probabilities with theoretical probabilities and decide whether the empirical probabilities are consistent with those predicted by theory.
Understand Bayes' Theorem, and how it can be used to find conditional probabilities.
High School Statistics | Combinations
Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting (the Basic Counting Principle).
Determine the number of possible arrangements (permutations) of a list of items
Calculate the number of possible permutations (nPr) of n items taken r at a time
Calculate the number of possible combinations (nCr) of n items taken r at a time
Differentiate between situations requiring permutations and those requiring combinations
High School Statistics | Statistics
Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles
Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none)
Understand the difference between correlation and causation
Identify variables that might have a correlation but not a causal relationship
Recognize how linear transformations of one-variable data affect the data's mean, median, mode, and range
Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation
Compare and contrast the appropriateness of different measures of central tendency for a given data set
Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data
Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot
Create a scatter plot of bivariate data
Construct manually a reasonable line of best fit for a scatter plot and determine the equation of that line
Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot
Use the normal distribution as an approximation for binomial probabilities
Calculate measures of central tendency with group frequency distributions
Calculate measures of dispersion (range, quartiles, interquartile range, mean deviation, standard deviation, variance) for both samples and populations
Know and apply the characteristics of the normal distribution
Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate
Determine the function for the regression model, using appropriate technology, and use the regression function to interpolate and extrapolate from the data
Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship
Use the Standardized Normal distribution table.
Calculate the mean from a frequency table.
In relation to the Normal Distribution, understand what is meant by the 1 sigma, 2 sigma and 3 sigma limits and how to calculate them.
Understand what is meant by the Standard Normal Distribution; and know how to standardize a Normal Distribution with known mean and standard deviation.
Understand what is meant by an Outlier and how it can affect the values of the mean, median and mode.
Understand that data can be positively or negatively skewed, or have no skew (as in the case of the Normal Distribution).
Know how to construct a grouped frequency distribution, and make decisions on the optimum size of each group.
Calculate the value of the Pearson Correlation Coefficient from a set of bivariate data
Know how to calculate the mean, variance and standard deviation of the Binomial Distribution.
Use data from a random sample to estimate a population mean and standard deviation, and understand the possible error in the estimates.
Compare data using tests of significance.
Define a random variable as a set of possible values (sample space) from a random experiment; graph the corresponding probability distribution (discrete random variables).
Calculate the mean (Expected value), variance and standard deviation of a discrete random variable.
Calculate a weighted mean.
Make unbiased selections by using a random method e.g. drawing lots or using a random number generator (or table).
Investigate simple continuous random Variables and their probability density functions, including the Uniform Distribution and use this as an introduction to the Standardized Normal Distribution.
Know how to find confidence intervals; in particular 95% and 99% confidence intervals for the Normal distribution.
Understand how to use the Chi-Square test for categorical data, how to use the Chi-Square Calculator to find the values of Chi-square and p, and use p to decide whether two variables are independent or not independent.