# 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.*

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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

☐ Quincunx

☐ 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

☐ Quincunx

☐ 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

☐ Quincunx

☐ 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

☐ 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.

☐ Outliers

☐ 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.