Statistics I - Describing Qualitative Data

Describing Qualitative Data

Key Terms

• Class: A category into which qualitative data can be classified.
• Class Frequency: The number of observations in the data set falling into a particular class.
• Class Relative Frequency: The class frequency divided by the total number of observations in the data set.
• Class Percentage: The class relative frequency multiplied by 100.

Question 1

In an eye color study, 25 out of 50 people in the sample had brown eyes. What does the number 0.50 represent?

• Answer: C) a class relative frequency

Summary Table

• Lists categories and the number of elements in each category.


• Obtained by tallying responses in each category.


• May show frequencies (counts), percentages, or both.


• Example:
  

• Uses vertical bars to represent qualitative variables.
• Bar height shows frequency or percentage.
• Zero point is used.
• Equal bar widths.

Pie Chart

• Shows the breakdown of a total quantity into categories.
• Useful for showing relative differences.
• Angle size is calculated as: (360°)(\text{percent})
• Example: If Economics represents 10%, Management 25%, and Accounting 65%, then the angle for Economics is (360°)(10\%) = 36°

Pareto Diagram

• Similar to a bar graph, but categories are arranged by height in descending order from left to right.
• Vertical bars represent qualitative variables.
• Bar height shows frequency or percentage.
• Zero point is used.
• Equal bar widths.

Example: 50 Highest Paid CEOs

• Data is provided on the degrees of 50 highest paid CEOs. The task is to construct a bar graph, pie chart, and Pareto diagram to describe the data.

Bar Graph Solution

• A bar graph displays the frequency of each degree type (Bachelor's, Law, MBA, Master's, None).

Pie Chart Solution

• A pie chart shows the percentage breakdown of degree types among the 50 CEOs, including MBA (40.0%), Bachelor's (38.0%), Master's (10.0%), Law (4.0%), and None (4.0%).

Pareto Diagram Solution

• A Pareto diagram displays the degree types in descending order of percentage, with MBA (40%), Bachelor's (38%), Master's (10%), Law (4%), and None (4%).

Question 2

What number is missing from the table?

Answer: 440

The calculation is \frac{600 \times 0.22}{0.30} = \frac{560 \times 0.22}{0.28} = \frac{400 \times 0.22}{0.20} = 440

Question 3

The pie chart shows the classifications of students in a statistics class. What percentage of the class consists of freshmen, sophomores, and juniors?

Answer: 10 + 46 + 30 = 86%

Microdata

A table of microdata is presented, including variables such as City, Gender, Age, Marital Relationship, Industry of Working Place, Occupation, and Annual Income (yen) for various individuals.

Cleaned Microdata

• A cleaned version of the microdata table is presented with some corrections, such as "Deirector" corrected to "Director" and "Rice Field" instead of "House".

Classifications

• Involve a set of discrete categories assigned to a specific variable.
• Used in statistical surveys or administrative files for producing and presenting statistics.
• Typically divide a variable into mutually exclusive and collectively exhaustive categories.

Examples of Classifications Led by United Nations Statistical Division

• Area: Standard Country or Area Codes for Statistical Use
• Industry: ISIC (International Standard Industrial Classification of All Economic Activities)
• Product: CPC (Central Product Classification), SIEC (Standard International Energy Product Classification)
• Trade: SITC (Standard International Trade Classification), BEC (Classification by Broad Economic Categories)
• Expenditure: COICOP (Classification of Individual Consumption According to Purpose), COPP (Classification of the Outlays of Producers According to Purpose), COFOG (Classification of Functions of Government), COPNI (Classification of the Purposes of Non-Profit Institutions Serving Households)
• Time: ICATUS (International Classification of Activities for Time-Use Statistics)

Examples of Classifications Led by World Health Organization (WHO)

• Medicine: ICD (International Statistical Classification of Diseases), ICF (International Classification of Functioning, Disability, and Health), ICHI (International Classification of Health Intervention), ICD-O (International Statistical Classification of Diseases for Oncology). Also includes classifications for mental and behavioral disorders, dentistry, neurology, primary care, external causes of injury, and the Anatomical Therapeutic Chemical Classification System.

Examples of Classifications Led by Other International Agencies

• Labour: ISCO (International Standard Classification of Occupations), ICSE (International Classification of Status Employment)
• Trade: HS (Harmonized Commodity Description and Coding System), NST (Classification Systems Used in Transport Statistics)
• Agriculture: Commodity Classification
• Education: ISCED (International Standard Classification of Education)
• Crime: ICCS (International Classification of Crime for Statistical Purposes)
• Activity: Classification of Statistical Activities

ISIC (International Standard Industrial Classification of All Economic Activities)

• Examples include: Agriculture, forestry and fishing; Mining and quarrying; Manufacturing; Electricity, gas, steam and air conditioning supply; Water supply; sewerage, waste management and remediation activities; Construction; Wholesale and retail trade; Transportation and storage, etc.

ISCO (International Standard Classification of Occupations)

• Examples include: Managers; Professionals; Technicians and associate professionals; Clerical support workers; Service and sales workers; Skilled agricultural, forestry and fishery workers; Craft and related trades workers; Plant and machine operators, and assemblers; Elementary occupations; Armed forces occupations.

Coding on ISCO Example: Workers in a Burger Shop

• 1412 Restaurant Managers
• 5120 Cooks
• 5246 Food Service Counter Attendants
• 9112 Cleaners and Helpers in Offices, Hotels and Other Establishments

Summary

• Bar graph: Categories of a qualitative variable are represented by bars, where the height represents class frequency, relative frequency, or percentage.
• Pie chart: Categories are represented by slices of a pie, with slice size proportional to the class relative frequency.
• Pareto diagram: A bar graph with categories arranged by height in descending order.

Notification for the Next Class

Prepare PC with Excel function. Ensure Excel is installed and functioning on your personal computer for the next class, as it will be used for practical exercises.