Stat Chapter 3

Title/Caption

Title/caption: The graph should have a title or caption (or both) that explains what is being shown and, if applicable, lists the source of the data.

Pareto Chart

A bar graph in which the bars are arranged in frequency order is often called a Pareto chart. Pareto charts make sense only for data at the nominal level of measurement.

Bar Graph

A bar graph is one of the simplest ways to picture a distribution. Bar graphs are commonly used for qualitative data. Each bar represents the frequency (or relative frequency) of one category: the higher the frequency, the longer the bar. The bars can be either vertical or horizontal.

Dotplot

A dotplot is a variation on a bar graph in which we use dots rather than bars to represent the frequencies. Each dot represents one data value.

Histogram

A graph in which the bars have a natural order and the bar widths have specific meaning, is called a histogram. The bars in a histogram touch each other because there are no gaps between the categories. A histogram is a bar graph showing a distribution for quantitative data (at the interval or ratio level of measurement); the bars have a natural order and the bar widths have specific meaning

Time-Series Diagram

A histogram or line chart in which the horizontal axis represents time is called a time-series diagram

Line Chart

A line chart shows a distribution of quantitative data as a series of dots connected by lines. For each dot, the horizontal position is the center of the bin it represents and the vertical position is the frequency value for the bin.

Multiple Bar Graph

A multiple bar graph is a simple extension of a regular bar graph: It has two or more sets of bars that allow comparison between two or more data sets. All the data sets must have the same categories so that they can be displayed on the same graph.

Multiple Line Chart

A multiple line chart follows the same basic idea as a multiple bar chart, but shows the related data sets with lines rather than bars

Stack Plot

Another way to show two or more related data sets simultaneously is with a stack plot, which shows different data sets in a vertical stack. Although data can be stacked in both bar charts and line charts, the latter are much more common.

Percentage Change Graphs

Graphs that show percentage change are very common, particularly with economic data. Although they are perfectly honest, you can be easily misled unless you interpret them with great care.

Horizontal Scale and Label

Horizontal scale and label: The categories should be clearly indicated along the horizontal axis. (Tick marks may not be necessary for qualitative data, but should be included for quantitative data.) Include a label that describes the variable shown on the horizontal axis.

Legend

Legend: If multiple data sets are displayed on a single graph, include a legend or key to identify the individual data sets.

A basic frequency table has two columns:

One column lists all the categories of data The other column lists the frequency of each category, which is the number of data values in the category

Pictographs

Pictographs are graphs embellished with additional artwork. The artwork may make the graph more appealing, but it can also distract or mislead.

Pie Charts

Pie charts are usually used to show relative frequency distributions. A circular pie represents the total relative frequency of 100%, and the sizes of the individual slices, or wedges, represent the relative frequencies of different categories. Pie charts are used almost exclusively for qualitative data. A pie chart is a circle divided so that each wedge represents the relative frequency of a particular category. The wedge size is proportional to the relative frequency. The entire pie represents the total relative frequency of 100%.

Geographical Data

Raw data that correspond to different geographical locations.

Cumulative Frequency

The cumulative frequency of any category is the number of data values in that category and all preceding categories.

Distribution

The distribution of a variable refers to the way its values are spread over all possible values. We can summarize a distribution in a table or show a distribution visually with a graph.

Relative Frequency

The relative frequency of any category is the proportion or percentage of the data values that fall in that category: relative frequency = frequency in category/total frequency

Stem-and-Leaf-Plot (stemplot)

The stem-and-leaf plot (or stemplot) looks somewhat like a histogram turned sideways, except in place of bars we see a listing of data for each category. Another type of stem-and-leaf plot lists the individual data values.

Vertical Scale and Label

Vertical scale and label: Numbers along the vertical axis should clearly indicate the scale. The numbers should line up with the tick marks—the marks along the axis that precisely locate the numerical values. Include a label that describes the variable shown on the vertical axis.

Binning Data

When it is impossible or impractical to have a category for every value in a data set, we bin (or group) the data into categories (bins), each covering a range of possible data values.