Probability & statistics - part 2

1.1.    Qualitative and Quantitative Data

Qualitative Data: Labels or names used to identify an attribute of each element are called qualitative data. These are often referred to as categorical data and use either the nominal or ordinal scale of measurements. Qualitative data can be either numeric or non numeric and appropriate statistical analyses for them are rather limited.

Quantitative data: Indicate how many or how much. If measuring how many, they are called discrete data and if measuring how much, they are called continuous data. Quantitative data are always numeric and ordinary arithmetic operations are meaningful for them.

1.2.    Data Summarisation : Graphical Methods

Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data. Different graphical techniques are available for different types of data.

Summarizing Qualitative Data

The only allowable calculation on qualitative data is to count the frequency of each category of a variable. When the raw data can be naturally categorized in a meaningful manner, we can display frequencies by

·         Bar charts – emphasize frequency of occurrences of the different categories.

·         Pie chart – emphasize the proportion of occurrences of each category.

Bar Charts

A bar chart can be used to depict any level of measurement: nominal, ordinal, interval, or ratio.

Example : The number of students enrolled in a management faculty  for a particular year is given below according to the subject streams they have selected. 

Program	Number of Students
Accounting	200
Financial Planning	250
Management Studies	275
Industrial Relations	150
Marketing	290

The qualitative variable contains five categories: Accounting, Industrial Relations, Financial Planning, Marketing, and Management Studies. The frequency (number of students) for each category is given. As the variable is qualitative, we select a bar chart to depict the data.

With this chart, it is easy to see that the highest enrollment is in Marketing and the lowest is in the Industrial Relations program.

Pie Chart

A pie chart, like a bar chart, is also used to summarize qualitative data. The pie chart is a circle, subdivided into a number of slices that represent the various categories. The size of each slice is proportional to the percentage corresponding to the category it represents.

Because the areas of the sectors, or “slices,” represent the relative frequencies of the categories, we can quickly compare them.  With this chart also, it is easy to see that the highest enrollment is in Marketing and the lowest is in the Industrial Relations program.

Summarizing Quantitative Data

There are several different ways of displaying quantitative data as they are given in numbers. This section introduced the basic methods of descriptive statistics used for organizing a set of numerical data in tabular form and presenting it graphically.

Some of the main descriptive methods for quantitative data include,

·         Stem and leaf display.

·         Frequency Tables.

·         Histogram.

·         Box plot

·         Scatter Diagrams

Next lesson for : main descriptive methods

Laahiru C.fernando.