2.2 Stem & Leaf Plots, Dot Plots and Shape

2 Stem-and-Leaf Displays Stem-and-leaf displays contain more information than frequency distributions and histograms. Consider the final-exam scores of 20 psychology students below: Find the leading digits of the numbers. Place these five numbers, called the stems, in a column: Now consider the ones place of each data value. Place this number, called the leaf, next to its stem

3 Dotplots A simple but effective graphical display is a dotplot. In a dotplot, each data point is represented by a dot above the number line. Below is a dotplot of the 20 management aptitude test scores. Dotplots are useful for comparing two variables. Suppose an instructor taught two sections of a management course and gave a simulated MAT exam in each section. The two groups could be compared using dotplots.

4 Distribution Shape Frequency distributions are tabular summaries of the set of values that a variable takes. The distribution of a variable is a table, graph, or formula that identifies the variable values and frequencies for all elements in the data set. The shape of a distribution is the overall form of a graphical summary, approximated by a smooth curve. A distribution is symmetric if there is a line (axis of symmetry) that splits the image in half so that one side is the mirror image of the other. A distribution is skewed if it has a longer “tail” on one side of the image.

5 Distribution Shape Symmetric, bell-shaped Right-skewed Left-skewed