In the beginning of this course (in the very first lesson!), we learned how to distinguish between discrete and continuous data. Discrete data are, again, data with a finite or countably infinite number of possible outcomes. Continuous data, on the other hand, are data which come from an interval of possible outcomes. Examples of discrete data include the number of siblings a randomly selected person has, the total on the faces of a pair of six-sided dice, and the number of students you need to ask before you find one who loves Stat 414. Examples of continuous data include:
- the amount of rain, in inches, that falls in a randomly selected storm
- the weight, in pounds, of a randomly selected student
- the square footage of a randomly selected three-bedroom house
In each of these examples, the resulting measurement comes from an interval of possible outcomes. Recall that the measurement tool is often the restricting factor with continuous data. That is, if I say I weigh 120 pounds, I don't actually weigh exactly 120 pounds... that's just what my scale tells me. In reality, I might weigh 120.01284027401307 pounds... that's where the interval of possible outcomes comes in. That is, the possible measurements cannot be put into one-to-one correspondence with the integers.
In this lesson, we'll investigate (or in some cases, review?) ways of summarizing continuous data. We'll summarize the data graphically using histograms, stem-and-leaf plots, and box plots. We've already discussed a couple of ways of summarizing continuous data numerically via the sample mean and sample variance. Here, we'll investigate how to summarize continuous data numerically using order statistics and various functions of order statistics.
One more thing here.... we'll be learning how to summarize data by hand. In reality, you would rarely rarely rarely ever do that in practice. Maybe if you were stranded on a desert island? In reality, 999 times out of a 1000, you and I are going to use statistical software to calculate percentiles and to create histograms, stem-and-leaf plots, and box plots. What's important here is that you just get the idea of how such graphs are created and such statistics are calculated, so that you know what they tell you when you encounter them.
- To learn how to create and read a histogram.
- To learn and be able to apply the empirical rule to a set of data.
- To learn how to create and read a stem-and-leaf plot.
- To learn how to create and read a box plot.
- To learn how to use order statistics to determine sample percentiles.
- To learn how to calculate the five-number summary for a set of data.