Teaching Models

Graph Data

Collecting and organizing data in a useful way allows students to incorporate many skills into one activity. Organizing data in tables will not only help students to disseminate data collected, but to perhaps find a solution to a problem or a reoccurring pattern. Encouraging labeling and correct scaling in graphical representation will aid in further data analysis and comprehension (National Research Council, 2001). Finally, utilize the completed graphical representation to answer questions.

The teacher plays a crucial role in helping students formulate their questions. Teachers should ask probing questions to allow students to reflect on the research questions to be answered, to sort the important features and record it in tables, to reclassify any seemingly superfluous information, and to best represent results.

Clusters, Gaps, and Outliers A cluster is formed when several data points lie in a small interval. A gap is an interval that contains no data. An outlier has a value that is much greater than or much less than other data in the set. An outlier may significantly affect the mean of a data set. A single outlier will not affect the mode(s) and is likely to affect the median only slightly. Features such as clusters, gaps, and outliers are more easily seen when the data are shown on a line plot.

Graph showing outlier
  with outlier without outlier
Mean 4 2.875
Median 3 2.5
Mode 2 2

Box-and-Whisker Plots
A box-and-whisker plot can be used to show how the data in a set are distributed. To make a box-and-whisker plot, first order the data from least to greatest. Five measures need to be computed in order to make the plot. These are the lower extreme, the upper extreme, the lower quartile, the upper quartile, and the middle quartile.

The lower and upper extremes are the least and the greatest numbers respectively in the data set.

The middle quartile is the mean of the data set. The lower quartile is the median of the lower half of the data set. When a data set has an odd number of entries, the lower quartile is the median of the data that fall below the middle number of the set. The upper quartile is the median of the upper half of the data set. When a data set has an odd number of entries, the upper quartile is the median of the data that fall above the middle number of the set. The three quartiles divide the data set into four parts.

The box-and-whisker plot is drawn using the five measures computed. It summarizes the data and makes it easy to see where the data are spread out and where they are closer together.

Example:

Make a box-and-whisker plot for the data set below.
60, 63, 69, 71, 73, 82, 87, 89, 92, 96, 99
Box and whisker plot

Teaching Model 10.2: Frequency Tables and Histograms


Houghton Mifflin Math Grade 6