1: Statistics - Part 1
Data are all around us. Researchers collect data on the effectiveness of a medication for lowering cholesterol. Pollsters report on the percentage of Americans who support gun control. Economists report on the average salary of college graduates. There are many other areas where data are collected. In order to be able to understand data and how to summarize it, we need to understand statistics.
Suppose you want to know the average net worth of a current U.S. Senator. There are 100 Senators, so it is not that hard to collect all 100 values, and then summarize the data. If instead you want to find the average net worth of all current Senators and Representatives in the U.S. Congress, there are only 435 members of Congress. So even though it will be a little more work, it is not that difficult to find the average net worth of all members. Now suppose you want to find the average net worth of everyone in the United States. This would be very difficult, if not impossible. It would take a great deal of time and money to collect the information in a timely manner before all of the values have changed. So instead of getting the net worth of every American, we have to figure out an easier way to find this information. The net worth is what you want to measure, and is called a variable. The net worth of every American is called the population. What we need to do is collect a smaller part of the population, called a sample. In order to see how this works, let’s formalize the definitions.
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- 1.1: Statistical Basics
- Data are all around us. Researchers collect data on the effectiveness of a medication for lowering cholesterol. Pollsters report on the percentage of Americans who support gun control. Economists report on the average salary of college graduates. There are many other areas where data are collected. In order to be able to understand data and how to summarize it, we need to understand statistics.
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- 1.2: Random Sampling
- Now that you know that you have to take samples in order to gather data, the next question is how best to gather a sample? There are many ways to take samples. Not all of them will result in a representative sample. Also, just because a sample is large does not mean it is a good sample.
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- 1.5: Graphs
- Once we have collected data, then we need to start analyzing the data. One way to analyze the data is using graphical techniques. The type of graph to use depends on the type of data you have. Qualitative data use graphs like bar graphs, pie graphs, and pictograms. Quantitative data use graphs such as histograms. To create any graphs, you must first create a summary of the data in the form of a frequency distribution, which is created by listing all of the data values and how often they occurs.