9: Statistics, Describing Data
- Page ID
- 59975
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- 9.1: Presenting Categorical Data Graphically
- Categorical, or qualitative, data are pieces of information that allow us to classify the objects under investigation into various categories. We usually begin working with categorical data by summarizing the data into a frequency table. A frequency table is a table with two columns. One column lists the categories, and another for the frequencies with which the items in the categories occur (how many items fit into each category).
- 9.2: Presenting Quantitative Data Graphically
- Quantitative, or numerical, data can also be summarized into frequency tables. A histogram is a graphical representation of quantitative data. The horizontal axis is a number line. in the histogram, a bar represents values on the horizontal axis from that on the left-hand side of the bar up to, but not including, the value on the right-hand side of the bar. Some people choose to have bars start at 1/2 values to avoid this ambiguity.
- 9.3: Measures of Central Tendency
- Let’s begin by trying to find the most “typical” value of a data set. Note that we just used the word “typical” although in many cases you might think of using the word “average.” We need to be careful with the word “average” as it means different things to different people in different contexts. One of the most common uses of the word “average” is what mathematicians and statisticians call the arithmetic mean, or just plain old mean for short.
- 9.4: Measures of Variation
- There are several ways to measure the “spread” of a data set. The first is the simplest and is called the range. The range is the difference between the maximum value and the minimum value of the data set. A more sophisticated measure of variation is called standard deviation. The standard deviation is a measure of variation based on measuring the distance each data value deviates, or is different, from the mean.
- 9.5: Exercises
- This page contains 17 exercise problems related to the material from Chapter 9.