Introduction to Statistics
Which would you prefer to see? This:
If you said the latter, you get an A for the day!
Statistics provides tools to use to get a picture from large amounts of data.
Getting the picture may involve using one or both of the following techniques:
(1) summarizing the data or
(2) looking at a part (a sample) of the data.
You just saw two of many possible data summaries: the average and range. We can use both these techniques together as did one of my former students, a bank auditor.
Even though all of the bank's transactions were on the computer, the auditor could not use such massive amounts of unorganized data to see how the bank was doing. Hence, she used both these techniques. First, she looked at only some of the records, called a sample of records. Second, she looked at several summaries of the data in the records sampled. Click the button to continue.
The most important aspect of dealing with data is to maintain a clear understanding of what the data represent. Then, you choose the correct statistical tools of sampling and summarizing to get the picture you need.
In statistics, formulas are far less important than common sense. Moreover, in this course, memorization will NOT be a component of your grade, but understanding will. For example, because you will work to understand how formulas relate to your picture, you will need to know what formulas you need, what numbers the formula requires, and thus where the numbers go into the formula.
If you cannot recall a formula, look it up, just as you do with phone numbers you can't recall!
Understanding the nature and purpose of the data and summaries is the key to acquiring this understanding and ability to apply your understanding. IN FACT, YOU WILL FIND UNDERSTANDING COMES MOST EASILY IF YOU VISUALIZE YOURSELF COLLECTING THE DATA DESCRIBED.
Let's look at one application that exemplifies how "visualizing" helps with the solution. Click on the button to view the example.
Ex. A sample of taxpayers is collected with the help of the IRS. The IRS official tabulated the data in the sample and found that 30% of the tax payers are single. What are the data the sample?
In some other math courses, you might expect that the answer would be the description of the value 30%, but that's not so here. We must imagine that we don't know the 30%. How would you go about obtaining this number? You must visualize collecting data and then you will know what the data are.
To visualize collecting data, we must first know how data are collected and what data are. To collect data in a sample, you must ask a person or object (called a "unit") in the sample a question about some quantity or characteristic (called a variable) and record the answer (data). The answer or response is one data value. The number of data values you get for a variable is the same as the number of times you ask a question about that variable. Remember, one data value corresponds to one sample unit!
Let us consider a sentence that describes the process of collecting the data. We consider this sentence in two forms.Technical version of sentence: "You ask a unit a question about a variable and record the data."
Now we want to visualize ourselves collecting each data value. Remember, to collect a single data value, you must get information from a single person or thing. To visualize in detail, we need the answers to two vital questions:
A. Who would you ask to get the information?
B. What question would you ask them?(Play "Jeopardy". If a number is the answer, what was the question?)
The questions in bold above belong on your note cards under the topic: data. In this example you are starting to see how a course on word problems - real world applications - differs from computational math courses you may have had.
The key to solving a word problem is to organize the information presented in the problem or story. The first step to organizing is always "Start with the answer and work backward.". We started with the answer "data are answers to questions" and worked backwards to the sentence defining data. Now, all we have to do is to rewrite this sentence with details that relate to the story of the IRS and the sample of taxpayers! If our sentence makes sense, the sentence tells us what the data are.
Continue with the above plan of "working backward" by clicking on the button.