1.1 Definitions of Statistics, Probability, and Key Terms

ABOUT STATISTICS
The science of statistics deals with the collection, organization, analysis, interpretation, and presentation of data. We see and use data in our everyday lives.

  • Organizing and summarizing: Descriptive statistics. Two ways to summarize data are by graphing and by using numbers (for example, finding an average).
  • Drawing conclusions from “good” data using probability: Inferential statistics.

What is Statistics?

The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life.

PROBABILITY
Mathematical tool used to study randomness. It deals with the chance (the likelihood) of an event occurring. The theory of probability began with the study of games of chance such as poker.

What are some of the situations you have encountered probabilities/chances in life?

KEY TERMS

KEY TERMS

Population
all individuals, objects, or measurements whose properties are being studied

Parameter
a number that is used to represent a population characteristic and that generally cannot be determined easily

Sample
a subset of the population studied

Statistic
a numerical characteristic of the sample; a statistic estimates the corresponding population parameter

Variable
a characteristic/attribute of interest for each person or object

Categorical Variable
variables that take on values that are names or labels

Numerical variables
variables that take on values that are numbers

Sampling
process of selecting a portion (or subset) of the larger population and studying that portion (the sample) to gain information about the population

Representative sample
a subset of the population that has the same characteristics as the population

Proportion
the number of successes xx divided by the size of the data set (total number of data values)

Mean
the total of the data values divided by the size of the data set (total number of data values)

Average
also called mean; a number that describes the central tendency of the data

Review & Practice

Review: Identify the population and sample

Please complete the practice exercise Identify the population and sample.

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, and average is technically a center location. However, in practice among non-statisticians, average is commonly accepted for arithmetic mean.

PRACTICE

Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment program. Suppose that a new AIDS antibody drug is currently under study. It is given to patients once the AIDS symptoms have revealed themselves. Of interest is the average (mean) length of time in months patients live once they start the treatment. A researcher follows 40 patients with AIDS from the start of treatment until their deaths. The following data (in months) are collected.

3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24; 18; 47; 33; 34

License

Icon for the Creative Commons Attribution-ShareAlike 4.0 International License

Statistics Study Guide Copyright © by Ram Subedi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

Share This Book