Analyzing and Representing Data: When Students Ask

• Why do I need to know how to represent data?
Organizing and representing data in charts, tables, and graphs is an important skill that helps students discover patterns and relationships and communicate numerical information to others. Different graphs displaying the same data can convey different messages, so selecting the graph that best represents the data is important. Knowing how to construct and use graphs will help your students interpret data presented to them in newspapers, magazines, and on television.
• How do I know which type of graph to use?
Some general guidelines are available, but there are no definite rules for selecting the “right” kind of graph for a given data set. If the data are continuous, such as the price of a stock over time, then a line graph is a good choice. If the data are discrete, then a bar graph, histogram, stem-and-leaf plot, or box-and-whisker plot would be a good choice. If you want to be able to see the actual data points, then the stem-and-leaf plot is a good choice. If you'd like a visual model of the median, range, and distribution of the data, then a box-and-whisker plot is a good choice.
• Why do I need to know how to analyze data?
Analyzing data puts numbers into a meaningful context. People need to be able to interpret and analyze data in order to make informed decisions.
• When do you use the mode?
The mode is probably the least reliable measure of central tendency for numerical data. The most frequently occurring number may not be representative of the entire data set. However, when the data are categorical, or nonnumerical, such as data collected about favorite flavors of ice cream, favorite basketball teams, or the most common pet among sixth-graders in your school, mode is a meaningful measure of central tendency to use. Here, the flavor, the basketball team, or the pet that occurs most frequently among the choices is probably the best representation of the data set.