Math Forum | Urban Systemic Initiative

Exploring Data - All Levels || Student Center || Teachers' Place

### 1989 NCTM Standards: Statistics

In grades 5-8, the mathematics curriculum should include exploration of statistics in real-world situations so that students can -

• systematically collect, organize, and describe data;
• construct, read, and interpret tables, charts, and graphs;
• make inferences and convincing arguments that are based on data analysis;
• evaluate arguments that are based on data analysis;
• develop an appreciation for statistical methods as powerful means for decision making.

Focus: In this age of information and technology, an ever-increasing need exists to understand how information is processed and translated into usable knowledge. Because of society's expanding use of data for prediction and decision making, it is important that students develop an understanding of the concepts and processes used in analyzing data. A knowledge of statistics is necessary if students are to become intelligent consumers who can make critical and informed decisions.

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 display, analyze, compare and interpret different data sets, including data sets that are not the same size, 1) analyzing data to determine measures and appropriate uses of central tendencies (mean, median and mode), and explain why these measures are the same or different; 2) organizing and displaying single-variable data in appropriate graphs and representations (e.g., histogram, line graphs, circle graphs) and explaining which types of graphs are appropriate for different kinds of data sets; 3) using fractions and percentages to compare data sets of different size; and 4) identifying ordered pairs of data from a graph and interpreting the meaning of the data in terms of the situation depicted by the graph. Sample tasks: Use information on bedtimes to determine the truth of various statements, using the mean, median and mode.

Read California's final Grade Five Mathematics Content Standards

Students collect data using samples of a population and describe the characteristics and limitations of the samples, 1) comparing different samples from a population with the data from the entire population and explaining when it makes sense to use a sample; 2) identifying different ways of selecting a sample (e.g., convenience sampling, those who respond to a survey, random sampling) and which makes a sample more representative for a population; 3) analyzing data displays and explaining how the way the question was asked might have influenced the results obtained, and/or how the way the results were displayed might have influenced the conclusions reached; 4) identifying data displayed in the media that represent sampling and explain why the sample (and the display) may be biased; 5) identifying claims based on statistical data and, in simple cases, evaluating the validity of the claims; 6) explaining which measure of central tendency (mean, median, mode) is most representative for a given sample.

Read California's final Grade Six Mathematics Content Standards

Students collect, organize and represent data sets that have one or more variables and identify relationships among variables within a data set, 1) using a stem-and-leaf plot or box-and-whisker plot to display a single set of data or compare two sets of data; and 2) representing two numerical variables on a scatter plot and informally describing how the data points are distributed and whether there is an apparent relationship between the two variables (e.g., time spent on homework and grade level).

Read California's final Grade Seven Mathematics Content Standards

Students analyze the trends in sets of bi-variate data, 1) summarizing trends in bi-variate data by informally fitting lines to data that appears to have a linear trend; and 2) evaluating the "goodness of fit" of a line for a set of data, assessing its usefulness as a model for the data and using the line to make predictions. Students also critique the conclusions and uses of statistics in both school materials and public documents, 1) using information displayed in graphs (line, bar, circle, and picture graphs and histograms) to make comparisons, predictions and inferences, and critique the conclusions drawn by others; and 2) explaining and critiquing the process of a survey or experiment, how that might have contributed to or influenced the results (e.g., reliability of sampling procedures, bias, missing or incorrect information), and describing misuses of statistical or numerical data.

Read California's final Probability/Statistics-Grades Eight Through Twelve Standards

### Philadelphia Standards: Using Data, Statistics, and Probability - Grades 8-5

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. Construct, read, and interpret tables, charts, and graphs incorporating the use of appropriate techniques and technology including line graphs, circle graphs, scatter plots, box and whisker plots, and stem-and-leaf plots.
2. Demonstrate and use measures of central tendency such as mean, median, and mode, and measures of variability such as range and quartiles.
3. Hypothesize conclusions and make convincing arguments based on data analysis.
4. Generate and analyze data that represent a sample of a given population.
5. Devise and carry out experiments that demonstrate the power of using a probability model.
6. Compare experimental results with mathematical expectations.
7. Generate and analyze graphical representations on a coordinate system.

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

• Shuffle a standard deck of 52 playing cards and count out 25 cards. Estimate the probability of drawing a club, diamond, heart, and spade. Do the experiment and compare the results with the estimate. Extend the experiment to 2,500 draws.
• Gather, analyze, and discuss data to determine the population density in various regions of the United States and other parts of the world.
• Record, individually or in groups, weather information from TV, newspaper, and radio using a chart or a spreadsheet. Compare the information graphically and discuss the conclusions.
• Evaluate and predict the sales performance of vendors at an amusement park when given specific data.
• Use USA Today graphs and determine the reliability of the statistics reported in the newspaper.
• Find and chart the median, mean, mode, and range of the daily attendance of the class for a one week period. Compare and discuss the results with another class.

Read the School District of Philadelphia's current Curriculum Frameworks

Questions? Write to the workshop facilitators.