In this unit, students will build on the knowledge and experience developed in the 6^{th} grade and 7^{th} grade univariate statistics units. (Bivariate data was the statistical focus in 8^{th} grade and Algebra 1.) “They will develop a more formal and precise understanding of statistical inference, which requires a deeper understanding of probability. Students learn that formal inference procedures are designed for studies in which the sampling or assignment of treatments was random, and these procedures may not be informative when analyzing non-randomized studies, often called observational studies.” (Progressions for the CCSS-M High School Statistics and Probability, p. 2)“Students now move beyond analyzing data to making sound statistical decisions based on probability models.” (Progressions for the CCSS-M High School Statistics and Probability, p.8). In addition, students will deepen their understanding of summarizing, representing and interpreting data on a single measurement variable by applying more complex measurement tools.
As in past data units, students: (1) formulate questions, (2) design a plan to collect data, (3) analyze data, and (4) interpret results/draw conclusions. This unit will build upon students’ understanding of statistical variability (quartiles, range, mean absolute deviation*(MAD), outliers) and their capacity to summarize and describe distributions (measure of center, shape) that were developed in middle school. They will now learn to give more precise answers to questions like deciding on which is the more appropriate measure of center, mean or median, and show their deeper understanding by justifying this choice using statistical reasoning. Two major shifts in focus and complexity from middle school to Algebra 2 are the ability to distinguish among distributions that were skewed or approximately symmetric to whether or not they are approximately normal as well as building on their understanding of MAD and applying it to the concept of standard deviation as a measure of variation.
Students will study data sets with generally normal distributions. In a normal distribution, the relationship between the mean, median and the percentages within one, two and three standard deviations from the mean are key to calculating and interpreting data. For a normal data set, students should be able to sketch a graph of the data distribution given information about the measure of center and the distribution and the reverse, describe the measures of center and distribution given a graph.
With respect to random sampling, students move beyond analyzing data, as they did in middle school, to making sound statistical decisions based on probability models. For example, students will apply their understanding of the mean and standard deviation of a data set to fit it to a normal distribution in order to estimate population percentages (S.ID.4). They will use their understanding of calculating margin of error in estimating a population quantity and extend it to the random assignment of treatments to available units in an experiment. Students will recognize the purposes of and differences among sample surveys, randomized experiments and observational studies as they make inferences and justify conclusions from real world contexts.
*NOTE: The mean absolute deviation (MAD), also called the average deviation of a data set {x_{1}, x_{2}, ..., x_{n}}, is the average of the absolute deviations and is an abstract statistic of statistical distribution or set of data.