Visual Representations of DAta

Visual summaries of data

1. Pie Chart

Used for showing divisions within a population, e.g., percentage of students in a QM class who own one of three types of pet.

2. Bar graph

Used in cases where one variable is made up of categories that are not numerically related and the other variable is numerical, e.g., the number of students (e.g., in an RM class) who prefer each of four types of music.

3. Histogram

Used when the scales used for both variables are numerical, e.g., the number of students who got a given mark on a class quiz or the height (numerical) compared to the frequency (numerical) of trees in a park.

5. Time series chart

Used to show change in quantities, over time, e.g., the number of immigrants to Canada from East Asia in the second half of the 20th century.

When should a bar graph be used and when should a histogram be used?


General rule of thumb

When one variable is a set of categories that are not numerically related, then a bar graph is used.  If both variables are measured on continuous scales, then a histogram is used.  Examples are given in the chart below.

Situation

Bar Graph or Histogram?

We want to compare total revenues of five different companies. Bar graph.  The five companies are categories, which are not numerically related to each other.  They are not points on a continuous scale.
We have measured revenues of several companies. We want to compare numbers of companies that make from 0 to 10,000; from 10,000 to 20,000; from 20,000 to 30,000 and so on. Histogram. Both variables are measured in terms of points (or are located within intervals) on a continuous scale.
We want to compare the number of trees of ten different species of trees in a city park. Bar graph.  The ten species of trees are not related to each other numerically.  They are not points on a continuous scale.
We have measured several trees in a city park. We want to compare the numbers of trees that are from 0 to 5 meters high; from 5 to 10; from 10 to 15 and so on. Histogram. Both variables are measured in terms of points (or are located within intervals) on a continuous scale.
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