The lesson explicitly teaches the definitions of population and sample and asks students to identify the attribute and population and decide whether data should come from the whole population or a sample (multiple activity pages and answer key). The lesson explains random sampling (e.g., randomly choosing 100 names, selecting every hundredth citizen, choosing players randomly from a registration list) and has activities where students choose which sampling methods are representative versus biased. The Parent Plan and activities state that random sampling tends to produce representative samples and support valid inferences about a population.

Students are asked in the Unit 8 Quiz to decide when data should come from a population or a sample, practicing classification of situations as population vs. sample. Students are asked to choose the least biased sampling method for finding the most popular pet, and the answer key identifies a random sample from the town census as the correct (non-biased) choice. Students complete activities that require organizing sample data into frequency tables and histograms, reinforcing use of sample data to describe distributions.

Students compute and interpret measures of variability (range, interquartile range, mean absolute deviation) and construct and read box plots across multiple activities. One activity states that "The water company randomly selected 100 homeowners" and asks students to identify the median, percent in a whisker, identify an outlier, and choose which new data value would be most typical, using the sample's box plot. Students complete calculations (MAD, IQR, range) on provided data sets and compare variability between two data sets (orchards, summer/winter births, snakes/lizards).

Students practice taking a random sample of candies (e.g., "reach into the package and pull out 10 candies") and use the sample counts to make inferences about the whole bag (predict most/least common colors and compare sample percentages to the population). In the word‑length activity students generate two samples (every 20th word and every 15th word), compute sample means, and compare those sample means to the actual mean word length (655 letters/183 words ≈ 3.6). The materials explicitly teach sampling variability and the effect of sample size (noting that increasing sample size decreases sampling variability) and ask students to reflect on which sample is closer to the population mean.

Students are prompted to use data from samples (e.g., pumpkin, zucchini, cat/dog adoptions, heights) to compute means and mean absolute deviations and to create stacked dot plots and boxplots for comparative inference. The Parent Plan and skills list explicitly refer to "random samples" and instruct students to use measures of center and variability from those samples to draw informal comparative inferences about two populations. Students are guided to compute the difference between sample means and divide by the larger mean absolute deviation to gauge overlap and how convincing a difference is.

Students draw inferences from data collected by described random samples (for example, the Unit 8 test asks students to use a movie-goer random sample to infer the busiest day). Students compare multiple provided samples and reason about sampling variability (histogram pair asking whether samples show high or low sampling variability and how fewer parents surveyed would affect variability). Students identify and evaluate sampling methods (Samuel's pool study and the county fair activities ask students to name convenience, biased, and more representative methods such as every 5th or every 50th person) and compute measures (means, median, MAD) used to support informal comparative inferences (Opal vs Randall; fiction vs nonfiction books).

Students are prompted to create a statistical question about a numerical attribute, define the population, and record methods of data collection. Students collect data, organize it (tally, frequency table, sorted list), and create dot plots, histograms, and box plots. Students calculate measures of center (mean, median, mode) and measures of variability (range, interquartile range, mean absolute deviation) and answer analysis prompts including "What general inferences can you make about the population of your statistical study?". The project requires students to summarize the number of observations, describe how the attribute was measured, and present conclusions on a poster or slideshow.

Students perform repeated coin-flip experiments and record counts for heads and tails at several sample sizes (5, 10, 50, 100), convert counts to fractions/decimals/percentages, and compare experimental probabilities to the theoretical 0.5. Students calculate theoretical probabilities for spinners by counting favorable outcomes and express probabilities as fractions, decimals, and percents. Students list complete sample spaces for coins, dice, spinners, and marble draws, and they play a die-rolling prediction game that has them predict outcomes and track results over many trials.

Students perform random sampling by spinning a three-color spinner for 10, 50, and 100 trials and record tallies and totals. Students calculate experimental probabilities from their recorded counts (as fractions, decimals, and percents). Students use the experimental probability from the 100-spin sample to predict counts for a larger population (predicting outcomes out of 600 spins). The mixed review and optional poker activity ask students to compare experimental and theoretical probability and to observe outcomes over repeated rounds.

Students conduct repeated chance experiments and record sample data: they roll a six-sided die in three rounds (30, 60, 120 rolls) and compute relative frequencies, and they spin a non-uniform spinner 50 times to compute experimental probabilities. Students build probability models from observed counts (e.g., fine arts choices: 16 choir, 10 band, 8 orchestra) and use those models to make predictions about expected counts. The lesson asks students to compare experimental results to theoretical expectations and discusses the Law of Large Numbers and possible sources of bias or error.

Activity 4 (Making Inferences) has students use a random sample (60 students) and compute a sample proportion (14/60 ≈ 23.3%) and then apply that proportion to the full population (1,143) to estimate about 266 students. Multiple student activity problems ask learners to compute proportions from samples (e.g., 18 of 50, 12 of 30, 40 of 100) and multiply by a larger population to produce an inference. The parent plan and answer keys explicitly describe students finding a sample proportion and using it to estimate counts in larger populations.

Students use random tools (marbles, a 10-sided die, and random digits) to model real situations and collect data. In Activity 1 they repeat trials 10 times recording "pulls until Blue," and in Activities 2–4 they run 20 simulation trials recording the number of rolls until a target outcome and then compute averages or counts/percents (e.g., convert # of trials with 4+ rolls to a percent). Students write hypotheses, compare their predictions to experimental averages, and answer reflection questions about why some trials took longer.

Students compute experimental probabilities from sample data (e.g., rolling a die 60 or 100 times and finding the proportion of 6s or 3s) and compare these to theoretical probabilities (Questions 6 and 11 and their answer explanations). Students design and run simulations (e.g., run at least 10 trials to estimate how many draws until a red marble or a copper coin) and record simulation results (Problems asking to run trials and report results). Students are asked to create probability models from observed frequencies and to use lists, tables, and tree diagrams to represent sample spaces, supporting inference from sample outcomes to probability statements.

Students build a probability model from the shelter data by calculating percentages for each size/color combination (e.g., 3/60 × 100 = 5%). Students run simulations using a 10-sided die to model arrivals (mapping die faces to small black or large black dogs), record the number of rolls until success, repeat each simulation five times, and compute an average. Students are explicitly asked to compare the simulation results to the model's prediction and to compare which simulation usually takes more rolls.

Students calculate experimental probabilities from a single simulated sample (spinner spun 25 times with yellow landing 7 times) and convert that frequency to a fraction and decimal. Students compare experimental and theoretical probabilities (e.g., marble bag, 8-sided die, game with theoretical 1/4) and explain why experimental results may differ due to chance. The Parent Plan and activities discuss designing and using simulations and observing long-run relative frequency (e.g., predicting wins in 20 trials and noting that experimental probability tends to the theoretical value as trials increase).

Students compute an experimental probability from a single series of trials in question 43 (spinner spun 25 times, yellow 7 times) and are asked to state the experimental probability (7/25) and explain how this might differ from the theoretical probability. Multiple items ask students to create probability models (question 44), list sample spaces for combined random actions (question 41), and draw tree diagrams for two-stage random experiments (question 46), so students practice modeling random processes and comparing experimental and theoretical outcomes.