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### 1989 NCTM Standards: Statistics

In grades 9-12, the mathematics curriculum should include the continued study of data analysis and statistics so that all students can -

• construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations;
• use curve fitting to predict from data;
• understand and apply measures of central tendency, variability, and correlation;
• understand sampling and recognize its role in statistical claims;
• design a statistical experiment to study a problem, conduct the experiment, and interpret and communicate the outcomes;
• analyze the effects of data transformations on measures of central tendency and variability;

and so that, in addition, college-intending students can -

• transform data to aid in data interpretation and prediction;
• test hypotheses using appropriate statistics.

Focus: Collecting, representing, and processing data are activities of major importance to contemporary society. In the natural and social sciences, data are also summarized, analyzed, and transformed. These activities involve simulations and/or sampling, fitting curves, testing hypotheses, and drawing inferences. To enhance their social awareness and career opportunities, students should learn to apply these techniques in solving problems and in evaluating the myriad statistical claims they encounter in their daily lives.

Read more about the 1989 NCTM Standards by logging in to my.nctm.org
Read the current Data Analysis and Probability Standard

### California Draft Standards: Statistics, Data Analysis, Probability

Students make inferences and predictions based on the analysis of a set of data and transformations performed on it, explaining the difference between the mean, mode and median with respect to the sensitivity of each measure to changes in the data set. Students also estimate relative frequency, compute probability, and demonstrate understanding of ways to make predictions from samples, and experiments in situations involving uncertainty, including dependent and conditional events, 1) using combinations and permutations to count the number of arrangements of a set of elements and distinguish between the two, and relate to the determination of theoretical probabilities; 2) demonstrating understanding of a random variable and how it can be used to make predictions about a population from a sample; and 3) graphing and interpreting probability distributions including the binomial distributions, and using them to discuss whether an event is rare or reasonably likely.

Students formulate and test hypotheses and demonstrate understanding that statistics is used to estimate the uncertainty involved in any conclusions which are drawn, 1) creating, implementing, defending a plan (including survey design, sampling procedures, control groups) for gathering data to answer a relevant question; 2) analyzing and evaluating surveys (for clarity, bias, return rate, specialized audiences) and experiments (for protocol, randomness, analysis, interpretation) done by others; 3) interpreting and evaluating graphical/tabular data displays for their consistency with the data and appropriateness of the type of display, scale and overall message; 4) describing a normal distribution and using it to predict such things as percentiles and probabilities; 5) demonstrating understanding that variability occurs between samples and that statistical analysis is a method by which this variability can be quantified.

Solve problems by interpreting data and predicting outcomes; make decisions based on the information collected, and clearly communicate the reasoning used to obtain the results.

BENCHMARKS: Grade-appropriate knowledge, skills and concepts ALL students achieve:

1. Describe the historical development of data collection, statistics, and probability from many cultures.
2. Use methods of statistical analysis to study data relevant to current civic, economic, or social issues.
3. Explore and choose measures of central tendency and dispersion to summarize and interpret single-variable data.
4. Analyze two-variable data using scatter plots, regression lines, and correlation coefficient.
5. Design a statistical experiment to study a problem reflecting the experiences of students and the larger community; conduct the experiment, interpret, and communicate the outcomes.
6. Gather, explore, and interpret data, graph ordered pairs; and graph and write the equation of a line for situations involving direct and indirect linear variation.
7. Describe, in general terms, the "normal distribution" curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.
8. Model mathematical situations, using simulations and experiments, to determine probabilities of independent and dependent events.
9. Use experimental and theoretical probability to represent and solve problems involving uncertainty.
10. Use curve-fitting to model and draw inferences about real data and situations.
11. Investigate careers which depend on the use of data, statistics, and probability.

PERFORMANCE EXAMPLES: The students may do ONE or MORE of the following as an example of a task that incorporates the benchmarks:

• Analyze a game (e.g., the state lottery) for "fairness" or "expected payoff."
• Discuss the uncertainty or likelihood of events occuring in the students' experiences.
• Determine what questions can be generated, given statistics reported in the media, in terms of how the data were collected and utilized to create the given statistics.
• Predict the results of a variety of track and field events for men and women athletes in future Olympic games, using data from previous Olympics, considering geographic locations.
• Prepare, individually or in groups, a financial profile comparing one restaurant with another. Enter into a database the salary of all employees. Determine the mean and standard deviation. If the employees receive a raise in pay, determine how this will affect the mean and standard deviation of the salaries.
• Choose, individually or in groups, a career which uses or a career person who uses, data, statistics and/or probability. Research, interview and/or shadow to understand how work place technology, environment or systems operate. Present and discuss at least two examples of how data, statistics, and/or probability are utilized (e.g., insurance actuarial, stock market, supply and demand, etc.).
• Select the best location for a school by evaluating such factors as distance, traffic patterns, population, density, and other appropriate data.