1. Presenting Categorical & Discrete Data
Chance & Data: Statistics
Presenting Categorical & Discrete Data
By the end of this lesson you will be able to explain/calculate the following:
Types of Data
Graphical Representation of Data

2. Types of Data All data can be divided into two major groups:
categorical (or qualitative) and numerical (or quantitative).
Placed in categories.
• nominal — the information is divided into subgroups;
for example, eye colour (hazel, blue, green).
• ordinal — the categories are in some type of ranked order;
for example, pizza sizes (family, large, medium, small).

3. Types of Data All data can be divided into two major groups:
categorical (or qualitative) and numerical (or quantitative).
Data are in numerical form.
• discrete — the data can take only certain exact values, usually whole numbers, and are associated with counting; for example, the number of SMS calls sent.
• continuous — the data can take any value within a certain range, and are associated with measuring; for example, the time taken to read Harry Potter and the Chamber of Secrets.

5. Graphs - Key Features Key features of graphs include:
a bold and appropriate title
clearly-labelled and evenly scaled axes
an attractive use of line, shading and colour
a key or legend for any symbols used, with roundings noted
a source of data which clearly identifies the origin of the information.

6. Bar and Column Graphs
Bar and column graphs are often used to represent categorical data
Each bar (or column) represents a single category or an observation
Its length (or height) shows the frequency of each category
The bar graph has frequencies on the horizontal axis
The column graph has frequencies on the vertical axis

7. Worked Example

10. Compound and Multiple Graphs
When comparing two or more sets of data relating to the same topic at the same time, the following are used:
compound column graphs and bar graphs
multiple column graphs and bar graphs.

13. Pie Graphs
Pie graphs (or sector graphs or pie charts or circular graphs) are mostly used to represent categorical data.
The size of the sector is proportional to the size of that category, as compared to the total.

14. Worked Example

17. Pictographs
Pictographs (or picture graphs or pictograms) allow data to be displayed in a novel way using illustrations or symbols
A key or legend is always used to show the number of items each symbol represents.
Half pictures can be used to represent half of the data.
However, smaller fractions such as one-third or one-quarter may be quite difficult to illustrate using pictographs

18. Worked Example

21. Dot Plots Dot-plots are similar to pictographs.
Each observation is represented by a single dot.
A good feature of the dot-plot is that it can be constructed while in the process of collecting the data.
A horizontal axis is prepared by writing in possible values of observations or categories, and then the collection of data begins.
Each time a certain value is observed, a dot is placed in the corresponding column.
Provided that the dots are placed neatly in columns and are evenly spaced, by the end of the experiment the data collected are also represented graphically

22. Worked Example