Statistics is still a complex limbo to many. When I first read the book, the ease of sharing logic was so awesome that I have kept it as one of my prized collections.

Offlate, I have started reading it again and I guess it is going to be great if I can share the details of the journey with my fellow enthusiasts.

The book: Introductory Business Statistics

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There are going to be excerpts from the book “Introductory Business Statistics” by Barbara Illowski. This material may be protected by copyright. I am not the owner of the content.

1. Statistics

Typically when you read any article or watch news, you are given sample information which helps you to make a decision about the correctness of the statement, claim, or “fact.” Statistical methods help in making the “Best Educated guess.” Generally, Statistics and Probability work together.

The science of Statistics deals with the collection, analysis, interpretation, and presentation of data.

1.1. Definitions of Statistics, Probability and Key Terms

1.1.1. Statistics
  • Descriptive: Organizing and summarizing data by graphing and by using numbers.
  • Inferential: The formal methods to draw conclusion from “good” data.
1.1.2. Probability
  • Mathematical tool to study randomness. It deals with the chance or “likelihood” of an event occurring.
1.1.3. Key Terms
  • Population: Complete collection of persons, things or objects under study.
  • Sample: The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population.
    • Statistic: Represents a property of the sample. It is an estimate of a population parameter.
    • Parameter: Numeric characteristic of the whole population that can be estimated by a statistic.
    • Variable: It is a characteristic or measurement that can be determined for each member of a population.
      • Numerical: Values with equal units. A discrete or continuous number. You do all mathematical calculations on it.
      • Categorical: They are essentially categories to classify your data. You show your final computation segregated by this.
Example:

Q: Tom and Hardy got 20 and 25 marks out of 30 in Science subject.

  1. Categorical Variable:
    • Tom
    • Hardy
    • Science
  2. Numerical Variable:
    • 20
    • 25
    • 30
Data are the actual values of the variable. They may be numbers or they may be words. DATUM is a single value.

Note: The words “mean” and “average” are often used interchangeably. The substitution of one word for the other is common practice. The technical term is “arithmetic mean” amd “average” is technically a center location. However, in practice among non-statisticians, “average” is commonly accepted for “arithmetic mean.”

Example 1.1:
Determine what the key terms refer to in the following study. We want to know the average (mean) amount of money first year college students spend at ABC College on school supplies that do not include books. We randomly surveyed 100 first year students at the college. Three of those students spent $150, $200, and $225, respectively.

Solution 1.1:
  • The population is all first year students attending ABC College this term.
  • The sample could be all students enrolled in one section of a beginning statistics course at ABC College (although this sample may not represent the entire population).
  • The parameter is the average (mean) amount of money spent (excluding books) by first year college students at ABC College this term: the population mean.
  • The statistic is the average (mean) amount of money spent (excluding books) by first year college students in the sample.
  • The variable could be the amount of money spent (excluding books) by one first year student. Let X = the amount of money spent (excluding books) by one first year student attending ABC College.
  • The data are the dollar amounts spent by the first year students. Examples of the data are $150, $200, and $225.”