Organisation and Presentation of Data

Content:
Simple frequency distribution
Grouped frequency distribution
Cross-tabulation/ Contingency table
Secondary statistics
Stem and leaf

Tabulation

Type of table

1. Frequency table
2. Two-way table/contingency table/cross tabulations
3. General table

Example of tables:

1. Every table should have a short explanatory title at the top.

2. At the end you should put the source of the information you have used, whether it is based on your own survey or secondary data.

3. The unit of measurement should be clearly stated.

4. Use different rulings to break up a larger table – i.e., double lines or thicker lines may be used to ease the reading of a table.

5. If useful, insert both row totals and column totals

6. If the volume of data is large, 2 or 3 simple tables are better than one cumbersome one.  For example, it is not a good idea to subdivide the table in slide 4 again. This is because interpretation becomes difficult.

Simple frequency distribution

Let the blood types of 40 persons are as follows: 

O O A B A O A A A O B O B O O A O O A A A A A B A B A A O O A O O A A A O A O O A B

Grouped frequency distribution

If the discrete variable can have a lot of different values or the quantitative variable is the continuous variable, then the data must be grouped into classes (categories) before the table of frequencies can be formed. The main steps in a process of grouping quantitative variable into classes are:

1. Find the minimum and the maximum values variable have in the data. (Min: 5/6, Max: 10/11)
2. Choose intervals of equal length that cover the range between the minimum and the maximum without overlapping. These are called class intervals, and their end points are called class limits.
3. Count the number of observations in the data that belongs to each class interval. The count in each class is the class frequency.
4. Calculate the relative frequencies of each class by dividing the class frequency by the total number of observations in the data. 

Age (in years) of 102 people:  

34,67,40,72,37,33,42,62,49,32,52,40,31,19,68,55,57,54,37,32, 54,38,20,50,56,48,35,52,29,56,68,65,45,44,54,39,29,56,43,42, 22,30,26,20,48,29,34,27,40,28,45,21,42,38,29,26,62,35,28,24, 44,46,39,29,27,40,22,38,42,39,26,48,39,25,34,56,31,60,32,24, 51,69,28,27,38,56,36,25,46,50,36,58,39,57,55,42,49,38,49,36, 
48,44

Cross-tabulation 
In a two-way frequency table, the classes (or categories) for one variable (called row variable) are marked along the left margin, those for the other (called column variable) along the upper margin, and the frequency counts recorded in the cells. Summary of bivariate data by two-way frequency table is called a cross-tabulation or cross-classification of observed values. In statistical terminology two-way frequency tables are also called as contingency tables.

The diagram below shows the relationship between blood type and gender

Secondary statistics
This could be use when constructing a table to ease the interpretation of the table. Example of secondary statistics are: Percentage, rates, ratio, etc..


Stem and leaf diagram
This is used to group data into classes.

—As in a table, there should always be a title accompanying the stem and leaf diagram 

—The leaf should always consist of 1 digit.

—The stem and leaf should always have a key.

—A stem and leaf diagram can be considered as an alternative to the grouped frequency distribution.

—The stem and leaf has the advantage of preserving the data.

—However the stem and leaf is not suitable for large amount of data.