Lesson 1 of 15 · free to read
Statistics involves collecting and analyzing data, and key terms like population, sample, and data are defined and distinguished.
You read a news article claiming that a new diet helps people lose weight, but the article only surveyed 50 people. How can you trust that this applies to everyone?
The idea
Statistics is the science of collecting, analyzing, interpreting, and presenting data, and it relies on key terms like population, sample, and data.
Definition
statistics
The science that deals with the collection, analysis, interpretation, and presentation of data.
The field of study that involves gathering, examining, explaining, and showing data.
Statistics appears everywhere—in news, sports, education, and politics. When you read an article or watch a news program, you are often given sample information, and statistical methods help you make the best educated guess about whether a claim is correct.
Definition
dot plot
A simple graph consisting of a number line and dots (or points) positioned above the number line to show the frequency of each value.
A chart that places a dot above a number line for each occurrence of a value, letting you see how often each value appears.
Dot plot of average sleep times (in hours) for a class of students.
Dot plot of 14 values: 5, 5.5, 6, 6, 6, 6.5, 6.5, 6.5, 6.5, 7, 7, 8, 8, 9. Lowest 5, first quartile 6, median 6.5, third quartile 7, highest 9.
Look at where the dots pile up: most values cluster between 6 and 7 hours, with a few at 8 and one at 9, showing the typical sleep time and the spread.
In this course, you will learn to organize and summarize data. Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using 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 how confident we can be that our conclusions are correct.
Vocabulary· 2 terms
Probability is used in many real-world predictions, from weather forecasts to investment returns. For example, if you toss a fair coin 4,000 times, the outcomes will be close to half heads and half tails, even though a few tosses may not be exactly balanced. The expected theoretical probability of heads in any one toss is 1/2 or 0.5.
Vocabulary· 2 terms
In statistics, we generally want to study a population. To study the population, we select a sample. The idea of sampling is to select a portion (or subset) of the larger population and study that portion to gain information about the population. Data are the result of sampling from a population.
Vocabulary· 2 terms
These key terms
Recap
Say each point to yourself, then tap it to check.
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Adapted from Introductory Statistics 2e, © 2023 OpenStax, Rice University
Barbara Illowsky and Susan Dean
Licensed under CC BY 4.0. This course is an adaptation, not the original work.
Access for free at openstax.org/details/books/introductory-statistics-2e