Data Management

BIG IDEAS:

(taken from “Big Ideas by Dr. Small”):

1. To collect good first-hand data, you must decide what collection method is most suitable and how to best pose any questions required to collect the data.

2. To collect good second-hand data, you must be very clear on what you want to know and what source can be trusted to provide data.

3. Sometimes a large set of data can be usefully described using a summary statistic, usually a single meaningful number that describes the entire set or a combination of different statistics. The number might describe the values of individual pieces of data and/or how the data is distributed or spread.

4. Graphs are powerful data displays since visual displays quickly reveal information about data.

   • Pictographs, bar graphs, histograms, and stem-and-leaf plots are particularly useful for comparing the frequency of data in different categories.

   • Circle graphs are particularly useful for comparing the frequency of data in one category to the entire set of data, while still allowing for comparisons among categories.

   • Line graphs and scatter plots are particularly useful for showing relationships between two quantities and trends.

5. How the data is graphed (e.g. the use of different scales or intervals) can affect what conclusions are drawn from the data.

STUDENT LEARNING GOALS:

GOAL #1: I can differentiate between a variety of data management terms including representative and random samples, census, and population.

• VIDEO: What Makes a Statistical Question (Source: Khan Academy)

• VIDEO: Continuous, Discrete & Categorical Variables (Source: Study.com)

• VIDEO: Census versus Sample (Source: Berenice Acosta on YouTube)

• VIDEO: Representative (unbiased) Samples (Source: Khan Academy)

• VIDEO: Creating Random Samples (Source: Khan Academy)

GOAL #2: I can determine the mean, median and mode of a set of data and determine which is the best method of measuring central tendency.

• VIDEO: Methods of Central Tendency (Source: Khan Academy)

• VIDEO: Mean, Median, and Mode Example (Source: Khan Academy)

• VIDEO: Impact of Removing an Outlier on Central Tendency (Source: Khan Academy)

• VIDEO: Impact of Increasing an Outlier (Source: Khan Academy)

• VIDEO: Finding a Missing Number when given the Mean (Source: Khan Academy)

• QUIZ: Choosing the Best Method of Central Tendency (Source: Khan Academy)

• QUIZ: Mean, Median, and Mode I (Source: Nelson Education)

• QUIZ: Mean, Median, and Mode II (Source: Nelson Education)

GOAL #3: I can collect and organize data into tables which include all necessary titles and labels.

• VIDEO: Frequency Tables (Source: Khan Academy)

• QUIZ: Samples and Surveys (Source: Khan Academy)

• QUIZ: Avoiding Bias in Data Collection (Source: Nelson Education)

• PRACTICE: Creating Frequency Tables (Source: Khan Academy)

GOAL #4: I can select the most appropriate graph (including histograms and scatter plots) for a specific set of data.

• VIDEO: Different Ways of Representing Data (Source: Khan Academy)

• VIDEO: Misleading Graphs (Source: Khan Academy)

• QUIZ:Reading Graphs (Source: Nelson Education)

• QUIZ: Changing Graph Appearance (Source: Nelson Education)

• QUIZ: Choosing the Most Appropriate Graph (Source: Nelson Education)

GOAL #5: I can make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs.

• VIDEO: Interpreting Circle Graphs (Source: Stacie Smallwood YouTube)

• PRACTICE: Making Inferences (Source: Khan Academy)

• QUIZ: Communicating about Graphs (Source: Nelson Education)

• QUIZ: Finding Trends in Graphs (Source: Nelson Education)

CURRICULUM EXPECTATIONS:

• collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject, and record observations or measurements;

• organize into intervals a set of data that is spread over a broad range (e.g., the age of respondents to a survey may range over 80 years and may be organized into ten-year intervals);

• collect and organize categorical, discrete, or continuous primary data and secondary data (e.g., electronic data from websites such as E-Stat or Census At Schools),and display the data in charts, tables, and graphs (including histograms and scatter plots) that have appropriate titles, labels (e.g., appropriate units marked on the axes),and scales (e.g., with appropriate increments) that suit the range and distribution of the data, using a variety of tools (e.g., graph paper, spreadsheets, dynamic statistical software);

• select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph (i.e., from types of graphs already studied, including histograms and scatter plots);

• explain the relationship between a census, a representative sample, sample size, and a population (e.g., “I think that in most cases a larger sample size will be more representative of the entire population.”);

• read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., election data or temperature data from the newspaper, data from the Internet about lifestyles), presented in charts, tables, and graphs (including frequency tables with intervals, histograms, and scatter plots);

• demonstrate an understanding of the appropriate uses of bar graphs and histograms by comparing their characteristics (Sample problem: How is a histogram similar to and different from a bar graph? Use examples to support your answer.);

• compare two attributes or characteristics (e.g., height versus arm span),using a scatter plot, and determine whether or not the scatter plot suggests a relationship (Sample problem: Create a scatter plot to compare the lengths of the bases of several similar triangles with their areas.);

• identify and describe trends, based on the rate of change of data from tables and graphs, using informal language (e.g., “The steep line going upward on this graph represents rapid growth. The steep line going downward on this other graph represents rapid decline.”);

• make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs (Sample problem: Use data to make a convincing argument that the environment is becoming increasingly polluted.);

• compare two attributes or characteristics, using a variety of data management tools and strategies (i.e., pose a relevant question, then design an experiment or survey, collect and analyze the data, and draw conclusions) (Sample problem: Compare the length and width of different-sized leaves from a maple tree to determine if maple leaves grow proportionally. What generalizations can you make?);

• determine, through investigation, the appropriate measure of central tendency (i.e., mean, median, or mode) needed to compare sets of data (e.g., in hockey, compare heights or masses of players on defense with that of forwards);