Chapter 3: Organization and Presentation of Data

Raw data

Data in their original form, and not yet organized or processed

Array

An ordered arrangement of data according to magnitude

Frequency distribution

A way of summarizing data by showing the number of observations that belong in the different categories/classes

Two general forms of frequency distributions

• Single-value grouping

  • Classes are the distinct values of the variable

• Grouping by class intervals

  • Classes are the intervals

Conditions for single-value grouping

Appropriate for categorical data and quantitative variables with FEW distinct observations

Conditions for grouping by class interval

Approrpiate for variables measured on interval or ratio level

Guidelines for constructing FDT via grouping by class interval

1. Determine adequate number of classes (Sturges’ rule: K = 1 + 3.322 log n)

2. Determine range (R = highest minus lowest values)

3. Compute C’ = R / K

4. Determine class size by rounding off C’ to a convenient number

5. Choose lower and upper class limits

6. Determine succeeding class limits by adding the class size to the lower class limit of the previous class

7. Tally all observed values in each class interval

8. Sum the frequency column

Relative frequency

The class frequency divided by the total number of observations

Relative frequency percentage

Relative frequency multiplied by 100

Open class interval

A class interval with no class limit nor upper class limit

• e.g. first category as “less than or equal to __”

• e.g. last category as “greater than or equal to __”

Class boundary

True class limits; actual boundary of each class intervaL

Lower class boundary (LCB)

The halfway between lower class limit of the class & upper class limit of preceeding

Upper class boundary (UCB)

The halfway between the upper class limit of the class and the lower class limit of the next one

Class mark

The midpoint of a class interval

Frequency histogran

Shows the overall picture of the distribution of the observed values in the data set (as seen as vertical bars) → to show shape of distribution

Axes on a frequency histogram

• Horizontal axis: class boundaries

• Vertical axis: class frequency

Three modes of data presentation

• Textual presentation

• Tabular presentation

• Graphical presentation

Examples of Graphs

• Line charts

• Vertical bars chart

• Horizontal bar chart

• Pie chart

• Pictographs

• Statistical maps

Advantage of graphical presentation

It can exhibit possible associations among the variables and can facilitate the comparison of different groups

Line chart

Graph that highlights movement of a time series (inc./dec.), wherein the variable assumes a different value for each time period

• also used to compare the trend of two or more time series data

Vertical bar graph

Graph that highlights the magnitude of a time series (e.g. how big a variable is at a certain period)

• can be used to show data changing over a period of time among several items

Horizontal bar chart

A graph that highlights the distribution magnitude of categorical variables

• bars arranged according to length of bar

Pie chart

A graph that highlights percentage distribution of a categorical data

• used if categories are less than six

Pictograph

A graph similar to horizontal bar chart, and used to get the attention of a reader

• a picture represents a unit of value

Statistical map

A graph that shows statistical data in geographical areas

• figures may be ratio, rate, percentage, or indices.