Monthly Archives: November 2015
Common Calculator Mistakes
This video focuses on stats specifically, but some of the errors are applicable for other math classes as well: setting the window size correctly, how to deal with syntax errors and other uninformative error screens, not mixing up your minus signs.
Calculator Window & Zoom Settings
You may not realize this, but the "window" and "zoom" buttons are the most misunderstood buttons on your calculator, and they lead to 90% of the errors and frustration that students have with TI-83 & TI-84 calculators. This video shows you how to nail them, which is especially important in statistics since stats graphs seem to have the most confusing settings: Xscl, Yscl, etc.
Entering Stats Data Into Calculator
This video shows you how to enter statistics data -- such as that long series of numbers given to you in a typical stats problem -- into your TI-83 or TI-84 calculator's tables so that you can take advantage of its graphing and data-crunching abilities.
Overview of Stats On Calculators
This video covers all the menus and data-entry button-presses you'll need to handle basic statistics calculations and graphs on your calculator. Later videos cover the minutia of setting the right window, entering data, and avoiding common mistakes.
Histograms On Your Calculator
Now that you're already a master of drawing histograms by hand, we'll show you how you'll actually do them: on a calculator.
Graphing Frequency Histograms (Dot Plots)
Before you can do one of these histograms by hand, you first have to start with a frequency table, so if you haven't already watched that video, do so now!. Then the histogram is easy, just be sure to use class boundaries properly.
When a book or teacher refers to a frequency distribution, usually they're referring to the graphical representation of that distribution, which may have a "bell" or "normal" shape. Technically, that graph is a histogram, so this chapter covers how to produce those histograms, both by hand and on your calculator.
Cumulative Frequency Distribution
Yet another take on the glory which is frequency tables, this variety is useful in certain types of data. This video shows you how to convert a plain old frequency table into a shiny & new cumulative version.
Relative Frequency Tables
Once you already know how to rock frequency tables, the "relative" variety is just the type where the frequency column contains percentages or proportions rather than raw data, just to make it easier to digest for your reader.
How To Draw A Frequency Table
In this video we get into the nitty gritty of creating frequency tables. And there's plenty to go over, including the subtleties of how to select the number of classes and class width, as well as the one thing you absolutely never do when you cook these things up.
Frequency Table Vocab
This video covers some of the terms you'll need for frequency table problems (and distributions as well) such as: upper class limits, lower class limits, class boundaries, class midpoints, and class widths.
These are those tables where the data are sorted into ranges and then tallied. While these most definitely *look* like tables, some teachers call them distributions. These videos cover standard frequency tables, as well as relative and cumulative versions, and vocab such as upper and lower class limits, class midpoints, class boundaries, and class widths.
Uniform Distributions (for Discrete Variables)
Uniform distributions (aka constant distributions) are ones that are just a straight line rather than bell-shaped. The picture to the right is not a typo! For real-world examples of discrete uniform distributions (roulette, day of the month someone is born on), and how to use area to calculate probability for one of these, check this video out.
Bimodal Distributions
Sometimes spelled bi-modal, this term describes a distribution with two mountain tops instead of just one. Definitely can't assume these are normal enough to use most stats tests on!
Kurtosis & Skewness
Kurtosis and skew are just a couple of numbers you can use to quantify how a distribution is different from the ideal of the normal distribution. Kurtosis tells you whether it's spiky or flat-topped, whereas skewness is about whether the mountain tips left or right.
How To Read A Distribution Graph
A distribution graph -- such as the "normal distribution" -- is basically just a graphical representation of a frequency table. This video explains how distributions are basically just bar graphs on steroids, and how area under the curve can be related to frequency.
The videos in this chapter introduce the basics of what distribution graphs are and what you can figure out from them (hint: area=probability), then applies that knowledge to a bunch of situations, including bi-modal distributions, uniform distributions, kurtosis, skewness, etc.
Chebyshev’s Theorem
This is basically just like the Empirical Rule except that it works for any distribution, not just bell-shaped normal-ish distributions. It even works for bimodal distributions, though it's so vague that it barely matters.
The Empirical Rule
The Empirical Rule is just a really basic rule of thumb for estimating the width of a bell curve based on standard deviation, or estimating standard deviation based on a bell curve (divide the width of the bell by 4).