Discuss the different types of graphical representations (pie charts, bar charts, histograms, and polygons). What are the levels of measurement that can be used with each type of graphical representation?
What will be an ideal response?
A pie chart consists of a round “pie” shape divided into parts, or “slices,” where each slice represents a separate value of the variable. The size of each slice of the pie is proportionate to the frequency (or proportion or percentage of the total) for each value; that is, the greater the contribution that a given value makes to the total number of observations, the larger the slice of the pie for that value. The total area of the pie chart should equal the number of observations if you are graphing the frequencies: 1.0 if you are graphing proportions and 100 if you are graphing percentages. These are best used for nominal level data.
The bar chart is appropriate for the graphical display of qualitative data only (nominal and ordinal). A bar chart represents the frequencies, proportions, or percentages of each value by a vertical or horizontal bar. The width of the bar is equal to 1.0, and the height (or length for a horizontal bar chart) is equal to the value’s frequency, proportion, or percentage (it does not matter which because the shape will be the same regardless). When we make the width of the bar equal to 1 and the height (or length) equal to the value’s frequency (or proportion or percentage), the total area of a bar in a bar chart corresponds to the area represented by the frequency (or proportion or percentage) of that value.
A histogram is very much like a bar chart. It is a graph of bars where the width of each bar on the x axis is equal to one (1.0) and the height of the bar on the y axis is equal to the value’s frequency, percentage, or proportion. The histogram’s bars are connected to one another, indicating that the underlying measurement continuum is continuous and quantitative. The bars on a histogram are placed on the graph from lowest score to highest score. In the bar chart, the placement of the values along the x axis was arbitrary. These can be used with interval and ratio level variables. A polygon or line graph can be used with continuous data. With a polygon, the frequency (or percentage or proportion) is represented by point or dot above each score, rather than by a rectangular bar, where the height of the point corresponds to the magnitude of the frequency.
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