Introduction to Managerial Statistics

Key Terminology: Populations, Samples, and Variables

To perform any analysis, one must understand the relationship between the groups being studied and the types of information being collected.

Population vs. Sample

• Population: The entire collection of all possible observations of interest. For example, all students enrolled in a specific course during a term.
• Sample: A representative subset of the population selected for study.
• Sampling: The actual process or method used to select the sample from the population.
• Census: A method where data is collected from every single element in a population, rather than just a sample.

When we calculate a measure from a population, we call it a Parameter. When we calculate a measure from a sample, we call it a Statistic.

Understanding Variables

A Variable is an item of interest that can take on different values. Variables are classified into two main types:

1. Qualitative Variables: Non-numeric variables that cannot be measured, such as gender, religious affiliation, or marital status.
2. Quantitative Variables: Numerical variables that can be measured. These are further divided into:
   • Discrete Variables: Variables that assume only certain values, often with "gaps" between them (e.g., the number of bedrooms in a house).
   • Continuous Variables: Variables that can assume any value within a specific range (e.g., air pressure in a tire).

Scales of Measurement

The way we assign numbers to data depends on the properties of order, distance, and fixed zero. There are four distinct scales of measurement:

Note on the Ratio Scale: Because the ratio scale has a "fixed zero," you can say one value is "twice as much" as another. For example, a person who is 6 feet tall is twice as tall as someone who is 3 feet tall. This is not possible with an interval scale like temperature.

Data Sources and Collection

Data can be categorized based on its origin:

• Primary Data: Data collected directly by the investigator for a specific purpose. This involves planning (deciding on sample size and method) and measuring (using focus groups, interviews, or experiments).
• Secondary Data: Data that has already been gathered and compiled by others from published or unpublished sources. When using secondary data, it is vital to check for biases or misreporting.

Limitations of Statistics

While statistics is a powerful tool for forecasting and hypothesis testing, it is not infallible. Users should keep three limitations in mind:

1. It deals only with quantitative information and aggregates of facts, not individual data items.
2. Statistical results are often approximate rather than mathematically exact.
3. Statistics can be easily misused; therefore, it should be applied by experts with a proper understanding of the data types.