Informal Statistics

Section 2.1: Describing Location in a Distribution

    So, in this chapter, you learned some cool tricks to figure out where stuff lands on a mountain of numbers.  There are two main ways you cooked: percentiles and this wild thing called a z-score.

    Percentiles show you how much of the portion of land is below a certain height.  It's like marking off a chunk of it from the bottom.  You can use a dope cumulative relative frequency graph to visualize percentiles or values on the mountain if you like.  

    The z-score is the G.O.A.T at comparing numbers.  They tell you how far a number is from the average, but they use this fancy lingo called standard deviations.  They basically create their own unit of standard deviations and use it to compare numbers from different types of mountains - they put it on a unit we all can dig.  

    You also learned how to describe the shape, center, and length of a mountain when turning the numbers onto a different scale.  Adding or subtracting more stuff to each value moves the mountain to a completely different area, but doesn't change its shape or length.  On the other hand, multiplying or dividing the values changes everything but the shape.  

Section 2.2: Density and Normal Distributions

    So in this section, you learned how density curves can show you more about these special types of mountains called normal mountains (kind of ironic isn't it).  One thing you have to know about these big-shot mountains is that their area they take up always equals to 1.  

    They have equal lengths and heights on both sides of their single-peaked structure.  Like all mountains, they use dem z-scores to measure a portion of their area.  There is a crazy trick that comes with these mountains: about 68% of the area will be within 1 standard deviation from the center, 95% will be within 2 standard deviations, and a whopping 99.7% will be within 3 standard deviations.  This W trick is called the empirical rule.  

    Now, if your observations aren't exactly 1, 2, or 2 standard deviations from the center, chill out.  Table A's got your back.  Your technology buddies like TI-84 also can help you out.  Whether you're shading the curve or using your calculator, just make sure you're clear about what you're doing.  

    You also learned cool ways to check if mountains are normal.  Graphs like dotplots, stem-plots, and histograms can help, but the real MVP is the normal probability plot. The more straight it looks, the more normal the data is.