7.SP Statistics and Probability
More Grade 7 Standards |
Use random sampling to draw inferences about a population
7.SP.1. 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. Aligned Resources
7.SP.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. Aligned Resources
Draw informal comparative inferences about two populations
7.SP.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 10cm 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. Aligned Resources
7.SP.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. Aligned Resources
Investigate chance processes and develop, use and evaluate probability models
7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Aligned Resources
7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Aligned Resources
7.SP.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. Aligned Resources
a. Develop a uniform
probability model by assigning equal probability to all outcomes, and
use the model to determine probabilities of events. For
example, if a student is selected at random from a class, find the
probability that Jane will be selected and the probability that a girl
will be selected.
b. Develop a probability model (which may not be uniform) by
observing frequencies in data generated from a chance process.
For example, find the approximate probability that a spinning penny
will land heads up or that a tossed paper cup will land open-end down.
Do the outcomes for the spinning penny appear to be equally likely
based on the observed frequencies?
7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Aligned Resources
a. Understand that, just as
with simple events, the probability of a compound event is the fraction
of outcomes in the sample space for which the compound event occurs.
b. Represent sample spaces for compound events using methods such as
organized lists, tables and tree diagrams. For an event described in
everyday language (eg, "rolling double sixes"), identify the outcomes
in the sample space which compose the event.
c. Design and use a simulation to generate frequencies for compound
events. For example, use random digits as a simulation tool
to approximate the answer to the question: If 40 per cent of donors
have type A blood, what is the probability that it will take at least 4
donors to find one with type A blood?