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Sampling and Data: Statistics (edited: Teegarden)

Module by: Mary Teegarden Based on: Sampling and Data: Statistics by Barbara Illowsky, Ph.D., Susan Dean

Summary: This module introduces the concept of statistics, specifically the ability to use statistics to describe data (descriptive statistics) as well as draw conclusions (inferential statistics). An optional classroom exercise is included. Labs changed to incorporate mini-tabs.

The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives. To be able to use data correctly is essential to many professions and is in your own best self-interest.

Example

Suppose class members write down the average time (in hours, to the nearest half-hour) they sleep per night. Then create a simple graph (called a dot plot) of the data. A dot plot consists of a number line and dots (or points) positioned above the number line. For example, consider the following data:

• 5; • 5.5; • 6; • 6; • 6; • 6.5; • 6.5; • 6.5; • 6.5; • 7; • 7; • 8; • 8; • 9

The dot plot for this data would be as follows:

Figure 1
Frequency of Average Time (in Hours) Spent Sleeping per Night
Dot plot with hours of sleep on the X-axis and frequency on Y-axis

In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by numbers (for example, finding an average). After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from "good" data. The formal methods are called inferential statistics. Statistical inference uses probability to determine if conclusions drawn are reliable or not.

Effective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. 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.

Glossary

Data:
A set of observations (a set of possible outcomes). Most data can be put into two groups: qualitative (hair color, ethnic groups and many other attributes of population) and quantitative (distance traveled to college, number of children in a family, etc.). In its turn quantitative data can be separated into two subgroups: discrete and continuous. Roughly speaking, data is discrete if it is result of counting (a number of student of the given ethnic group in a class, a number of books on a shelf, etc.), and data is continuous if it is result of measuring (distance traveled, weight of luggage, etc.)
Statistic:
A numerical characteristic of the sample. Statistic estimates the corresponding population parameter. For example, the average number of full-time students in a 7:30 a.m. class for this term (statistic) is an estimate for the average number of full-time students in any class this term (parameter).

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