Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
Math.7.SP.2 or 7.SP.A.2
Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
Math.7.SP.3 or 7.SP.B.3
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
Math.7.SP.4 or 7.SP.B.4
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
An inference or generalization about a population can be made from a sample that is representative of the population.
For a sample to be representative:
The people in the sample are selected randomly.
The types of people in the sample are proportional to those in the population.
For the sample to be representative, the number of accounting, customer service, and sales employees in the sample needs to be proportional to the number of accounting, customer service, and sales employees in the company.
The employees in the sample also need to be randomly selected. So, randomly selecting 3 accounting employees, 5 customer service employees, and 2 sales employees would produce a representative sample.
Therefore, selecting every tenth employee from an alphabetical list of the names of the employees in each department would produce a representative sample.