Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, explanation, and presentation of data. Statistics has become much easier with the power of graphing calculators. Before powerful calculators, all the complicated calculations of statistics were done by hand.
The methods used in statistics developed from probability theory. Back in the late 17th century, Pierre de Fermat and Blaise Pascal wrote letters to friends laying out the basis for modern statistics. Originally statistics was thought of as a science, but by the early 18th century published documents started treating statistics as a branch of mathematics.
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Statistics is math that is used to learn about patterns in data. Data are not just numbers but numbers with meaning.
Here is an example of what I am talking about when I say "numbers with meaning". 95 is a number with no inherent meaning. If I am talking about math grades and say 95%, then you know you have a good grade. I have given meaning to the number. If I am talking about IQ and say you have an IQ of 95, then you know you are in the middle of the normal IQ range. If I take your pulse and it is 95 beats per minute, then your pulse rate is fast. In statistics, you need more than just a number, you also need information about the number, what it means, and how it is used.
The data you use and where it comes from will influence the answers that you get. You will need to be careful about drawing conclusions from data until you know about the data and are sure it is good data for the question you are trying to answer.
It is tempting to trust personal experience or to use a small amount of data when answering a question. You might think that students at CHS are typical of high school students everywhere, but they are very different from students in a big city high school or even a small rural school in a different part of the country. If you ask students at CHS to answer questions in a survey, you might get answers that represent CHS students. But you have to be careful that you don't assume that CHS students are typical of all high school students.
Data can be observational or experimental. If you stand at a corner and record the cars that drive by and how many people are wearing seat belts, then you are collecting observational data. A survey is another type of observational data. You could do a survey of students and ask them if they wear seat belts.
Statistical methods are mathematical methods used to summarize or describe collections of data. This is sometimes called descriptive statistics.
In real life applications, data is analyzed to see if patterns exist that can be explained. When studying the data, statisticians use the patterns to account for randomness. look for uncertainty, and draw conclusions (called inferences) about the process that created the data. This is called inferential statistics.
Descriptive and inferential statistics together are known as applied statistics. This kind of statistics is used in real life - engineering, politics, biology and environmental sciences, and many other applications. For real math geeks who only are interested in the theory of statistics, there is a branch called mathematical statistics.
Data used in statistics can come from a variety of sources. Most data used by students is observational data. This may be data you collect from watching something happen or it can be data someone else collected that you think might be useful for what you are studying.
An example of observational data would be a survey. Suppose you go to all your friends in the school and ask them how many hours of TV they watched on Monday night. This data would give you a good idea of TV viewing by your friends. It would not tell you about how much TV is watched overall by the students in your school, or by students your age from around the country.
Experimental data is collected from a study or experiment specifically designed to answer a particular question. In medicine, drug companies must do careful experiments to prove that a new drug works and does not cause harmful side effects. If you just went and asked people if they felt better you would not get good experimental data.
Sometimes you can use experimental data collected for another purpose to help answer other questions. In the United States, the Center for Disease Control (CDC) collects data on the cause of death of everyone in the country. From this data they look for patterns and then may do a specific experiment to get more specific data. It is known that there are "disease clusters" that occur in particular ethnic groups, but not as frequently in the general population. CDC data was used to justify a study that looked for gene markers on the DNA of people sick with the disease. Now that information can be used to treat people before they show symptoms so they can lead a longer and healthier life.
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