Frequency Distributions and Graphs Chapter 2

Other Types of Graphs 2 - 3

Bar Graph A bar graph represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data. A bar graph is used to graph data from a categorized (or qualitative) frequency distribution.

Bar Graph How to graph: For a horizontal bar graph, write the categories on the y-axis and the frequency scale on the x-axis. For a vertical bar graph, write the categories on the x-axis and the frequency scale on the y-axis. Draw the bars corresponding to the frequencies.

Compound Bar Graph A compound bar graph is a bar graph that compares data for two or more groups. The graph on the right compares data for men and for women. The bars for each category (year) for men and women are placed side by side. This allows the reader to compare data for men versus women.

Pareto Chart A pareto chart is used to represent a categorical frequency distribution, and the frequencies are displayed by the heights of vertical bars that are arranged in order from highest to lowest. How to graph: The categories are placed on the x-axis in order from highest frequency to lowest frequency. The frequencies are graphed on the y-axis.

Time Series Graph A time series graph represents data that occur over a period of time. How to graph: The time units are graphed on the x-axis. The frequency is graphed on the y-axis. Dots are connected but NOT connected to the x-axis.

Compound Time Series Graph Two or more data sets can be compared at the same time on a compound time series graph.

Pie Graph A pie graph is a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution. How to graph: Calculate the frequency percentage for each category. To calculate the angle measure of a section:

Dot Plot A dot plot is a statistical graph in which each data value is plotted as a point (dot) above the horizontal axis. A dot plot is used to see how the data values are distributed and to see if there are any extremely high or low data values.

Dot Plot How to graph: Find the highest and lowest values to determine the range of your data. Draw a horizontal line, and draw the range (scale) on the line. Plot each data value as a dot above the line. If the value occurs more than once, plot the other point above the first point.

Stem and Leaf Plots A stem and leaf plot is a data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes. How to graph: Arrange the data in order. Separate the data according to the first digit. The leading digit is the “stem” and the trailing digit is the “leaf”. “Leaf” values should be listed in order.

Back-to-Back Stem and Leaf Plot Related distributions can be compared using a back-to- back stem and leaf plot. The “leaf” values for one data set is graphed to the left of the stem. The “leaf” values for the second data set is graphed to the right of the stem.

Misleading Graphs Inappropriately drawn graphs can misrepresent data. Truncating the scale – Notice that in the top graph, the scale has been truncated. It shows a significant difference in data. The bottom graph is not truncated – the data are very similar. Changing the units at the starting point of the y-axis can convey a very different visual representation of the data.

Misleading Graphs It is not wrong to truncate an axis of the graph. The bottom graph shows a slight increase that is barely detectable in the top graph. The point is that you should check the starting point of the y-axis when you read a graph. Again, changing the starting point on the y-axis changes the visual representation. This is not wrong – we just need to be aware of it.

Misleading Graphs Exaggerating a one- dimensional increase by showing it in two dimensions: This can make an increase seem much larger to the eye than it actually is. It is not wrong to do this – the reader should just be cautious of the conclusions drawn on the basis of graphs.

Misleading Graphs Another way to misrepresent data on a graph is by omitting labels or units on the axes. Without labels and units on the y axes the graphs below show little more than a crude ranking of data.