Investigation 4: Collecting, Organizing, Displaying, and Interpreting Data
Data investigation involves four phases: collecting (gathering observations), organizing (sorting into tables or lists), displaying (creating graphs or charts), and interpreting (drawing conclusions). In Grade 6 Saxon Math Course 1 (Chapter 4: Number, Operations, and Measurement), students classify data as quantitative (numerical measurements such as height or score) or qualitative (categorical descriptions such as color or breed). They select appropriate displays—bar graphs for categories, line graphs for change over time, circle graphs for parts of a whole—and draw valid conclusions while identifying limitations of small sample sizes.
Key Concepts
New Concept Statistics is the science of gathering and organizing data to draw conclusions. Quantitative data is numerical (e.g., number of visits), while qualitative data is categorical (e.g., favorite sport). What’s next This lesson will guide you through worked examples on classifying data, creating visual displays like bar graphs, and analyzing real world survey questions.
Common Questions
What is quantitative data?
Quantitative data is numerical—values that can be counted or measured. Examples: test scores, heights, temperatures, number of goals scored.
What is qualitative data?
Qualitative data describes categories or qualities using words or labels. Examples: eye color, favorite subject, breed of dog.
What are the four steps of a data investigation?
1. Collect: gather data through surveys, experiments, or observation. 2. Organize: arrange data in tables, lists, or tally charts. 3. Display: create a graph or chart. 4. Interpret: analyze the display to draw conclusions.
Which type of graph is best for showing parts of a whole?
A circle graph (pie chart) is best for showing how categories divide a whole, since its sectors represent proportions of 360°.
Why does sample size matter when interpreting data?
Larger samples produce more reliable conclusions. A small sample may produce results due to chance that would not hold for the full population.