Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

1. Use one of the four basic sampling methods to distribute surveys appropriately. (Random, systematic, stratified, and cluster) a. MA.912.S.2.2: Apply the definition of random sample and basic types of sampling, including representative samples, stratified samples, censuses. b. CCSS.Math.Content.HSS-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population 2. Recognize and prevent faulty questions on a survey and other factors that can bias responses. a. MA.912.S.2.3: Identify sources of bias, including sampling and non-sampling errors 3. Develop a survey that accurately measures the data necessary to answer the driving questions. a. MA.912.S.1.1: Formulate an appropriate research question to be answered by collecting data or performing an experiment. b. MA.912.S.1.2: Determine appropriate and consistent standards of measurement for the data to be collected in a survey or experiment. c. MA.912.S.2.1: Compare the difference between surveys, experiments, and observational studies and what types of questions can and cannot be answered by a particular design. d. CCSS.Math.Content.HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each 4. Determine sample spaces and find the probability of an event, using classical probability or empirical probability. (students can find the classical probability before issuing the surveys and empirical probability once they have the results from the surveys) a. MA.912.P.2.2: Determine probabilities of independent events. b. MA.912.P.1.1: Use counting principles, including the addition and the multiplication principles, to determine size of finite sample spaces and probabilities of events in those spaces. c. MA.912.P.2.1: Determine probabilities of complementary events, and calculate odds for and against the occurrence of events. d. CCSS.Math.Content.HSS-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). e. CCSS.Math.Content.HSS-CP.B.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. f. CCSS.Math.Content.HSS-CP.B.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. 5. Find the probability of compound events, using the addition or multiplication rules. (Have the students look at the probability of when the consumer likes one thing or another; observe the case when things are mutually exclusive or not) a. MA.912.P.1.2: Use formulas for permutations and combinations to count outcomes and determine probabilities of events. b. CCSS.Math.Content.HSS-CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. c. CCSS.Math.Content.HSS-CP.B.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. 6. Find the conditional probability of an event. (this is the probability of an event given the outcome of another one; make sure that students ask if/then type questions; look at the candy example) a. CCSS.Math.Content.HSS-CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. b. CCSS.Math.Content.HSS-CP.A.3 Understand the conditional probability of A given B as P(A andB)/P(B), and interpret independence of A and B as saying that the conditional probability of A givenB is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. c. CCSS.Math.Content.HSS-CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations d. CCSS.Math.Content.HSS-CP.B.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. 7. Construct a probability distribution for a random variable. (A table of the probability of each event in the sample space before distribution) a. CCSS.Math.Content.HSS-MD.A.1 (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. b. CCSS.Math.Content.HSS-MD.A.2 (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. c. CCSS.Math.Content.HSS-MD.A.3 (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. d. CCSS.Math.Content.HSS-MD.A.4 (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value 8. Find the mean, variance, and standard deviation for the variable of a binomial distribution. (it looks a bit plug and chug, but may need this as above) a. MA.912.S.3.4: Calculate and interpret measures of variance and standard deviation. Use these measures to make comparisons among sets of data b. CCSS.Math.Content.HSS-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. 9. Organize (survey) data using a frequency distribution 10. Represent data in frequency distributions graphically using histograms, frequency polygons and ogives (none of these are appropriate for discrete categorical data collection; use for pricing preferences?) and using bar graphs, Pareto Charts, time series graphs, and pie graphs (good for discrete categorical stuff) a. CCSS.Math.Content.HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). b. MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following: i. bar graphs ii. line graphs iii. stem and leaf plots iv. circle graphs v. histograms vi. box and whisker plots vii. scatter plots viii. cumulative frequency (ogive) graphs 11. Draw and interpret a stem and leaf plot ( not good for discrete, but could work with continuous numbers) a. CCSS.Math.Content.HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). b. MA.912.S.3.1: Read and interpret data presented in various formats. Determine whether data is presented in appropriate format, and identify possible corrections. Formats to include: i. bar graphs ii. line graphs iii. stem and leaf plots iv. circle graphs v. histograms vi. box and whiskers plots vii. scatter plots viii. cumulative frequency (ogive) graphs c. MA.912.S.3.2: Collect, organize, and analyze data sets, determine the best format for the data and present visual summaries from the following: ix. bar graphs x. line graphs xi. stem and leaf plots xii. circle graphs xiii. histograms xiv. box and whisker plots xv. scatter plots xvi. cumulative frequency (ogive) graphs 12. Summarize data, using measures of central tendency, such as the mean, median, mode, and midrange. (Benchmark lesson or investigation?) a. MA.912.S.3.3: Calculate and interpret measures of the center of a set of data, including mean, median, and weighted mean, and use these measures to make comparisons among sets of data. 13. Find the mean, variance, standard deviation, and expected value for a discrete random variable. (Students can do this for each answer after distribution) a. MA.912.S.3.4: Calculate and interpret measures of variance and standard deviation. Use these measures to make comparisons among sets of data 14. Describe data, using measures of variation, such as the range, variance, and standard deviation. (Same as above) a. MA.912.S.3.4: Calculate and interpret measures of variance and standard deviation. Use these measures to make comparisons among sets of data 15. Justify whether or not the survey was an appropriate measure of data to answer the driving question. a. CCSS.Math.Content.HSS-IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. b. CCSS.Math.Content.HSS-IC.B.6 Evaluate reports based on data c. CCSS.Math.Content.HSS-MD.B.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game) CCSS.Math.Content.HSS-CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Common Core Math Glossary Terms: (Alphabetical Order) Independently combined probability models. Two probability models are said to be combined independently if the probability of each ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair. Mean. A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list.4 Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21. Mean absolute deviation. A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20. Median. A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11. Probability distribution. The set of possible values of a random variable with a probability assigned to each. Probability. A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition). Probability model. A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model. Random variable. An assignment of a numerical value to each outcome in a sample space. Rational expression. A quotient of two polynomials with a non-zero denominator. Sample space. In a probability model for a random process, a list of the individual outcomes that are to be considered. Uniform probability model. A probability model which assigns equal probability to all outcomes. See also: probability model.