Describing Dispersion or Measuring Spread
This is a summary of lecture four of the Teaching Company course Meaning from Data: Statistics Made Clear. The course is very basic but it has helped to improve and revise my understanding of statistics. All I can recall from introductory statistics at university was confusion and anxiety.
In order to get meaning from a bunch of numbers we need to look at the traits that the data have. Below is a diagram I created to assist in my description.
The mean and median are measures of central tendency. The mean is the ‘balancing point’ around which all data sit. Outliers have a effect on that balance. The median is the mid point of the data points and is not affected by outliers. Neither gives us an indication of how spread out the data are.
A histogram gives us an visual approximation of the spread of the data. A five-number summary gives an simple numerical summary of the data from which spread can be deduced but does not allow us to visualise the overall shape of the data the way a histogram can.
Standard deviation and variance give a single digit summary of how varied the data are relative to the mean.
The next diagram gives a mechanical representation of the way the data is processed in order to produce the standard deviation.
The mean as well as each of the data points are fed into the equation in order to produce a single standard deviation value. The limitations that are associated with expressing data using the mean are incorporated into the standard deviation value, that is, it also is susceptible to outliers.
Free Online Classes
I was directed to a compilation of free online classes from a gHacks.net post titled ‘Online Free Classes.’ So far, the ones on making and using rules and judges and the law look interesting. If I go through them, I’ll include a post or an aside on what they were like.
Grammar
I really really really should learn grammar. Really.
I Better Create a Post on This Before I Forget
Closeness and Confidence
Here is my summary of Meaning from Data: Statistics Made Clear Lecture Three. I made it using a combination of GIMP and Inkscape, so it’s not quite up to Photoshop standards. It shows a sample of stars randomly taken from a larger pool of stars. The information that can be inferred from the smaller sample about the larger one (that is, it’s shape, centre and spread) is limited in terms of ‘closeness’ and ‘confidence’. The aim of an experiment is to enable us to infer the characteristics of the complete data set with high closeness and high confidence. If closeness is high but confidence low then we will find that the estimates will often be outside the closeness limits. If the closeness is low but the confidence high then the estimates will be too vague to rely upon.
Data and Distributions
The following picture is a summary of lecture two of the Teaching Company series Meaning from Data: Statistics Made Clear. I produced it using Rationale and Photoshop. It has been saved in the Portable Network Graphics (PNG) format because that format is the most efficient for storing diagrams such as the one reproduced below.
Continuing Basic Maths Revision
I previously wrote that I am in the process of (quickly) going through the Teaching Company series High School Level—Basic Math as a form of revision. I have completed lectures 17 and 18. I might go through them again because I wasn’t fully concentrating.
I am using SlimTimer to keep a record of my activities but I’m not sure that I like this program that much. You see, I remembered that I had gone through a lecture the other day (but couldn’t record it at the time because the program wasn’t working properly) and wanted to add it at a later point but I am not sure it has properly been recorded as a completed task. It’s hard to tell. Also, I am doing separate tasks, all with a similar title but separate details, titled “Listen to Lecture”, every time I listen to a separate lecture. But I think that when I look at a summary the program sees them all as the same task rather than each being a separate task. And another thing, by pausing the task and starting it again, the program appears to record it as one task finishing and a new one is beginning when it should really be just the one task. The first picture below shows how a single session with several pauses has been recorded as several separate tasks (the bottom three rows). The one below that shows that the summary for the day is one long task rather than the two separate tasks I that intended – Listen to Lecture (Lecture 17) and Listen to Lecture (Lecture 18) (see the row for 27/6/2007).
Making a Start on a New Series
I started Meaning from Data: Statistics Made Clear today. Like most introductory lectures, there wasn’t anything too specific to remember. So far I’ve learnt that the two main purposes of statistics are to (1) describe or summarise a complete set of data to give it meaning and (2) to infer from a sample of a group the characteristics of the complete group. I’ve summarised these two main concepts using Photoshop below. Put simply, statistics involves giving meaning to otherwise meaningless data.
I am going to go back to the ‘Course Guidebook’ now and ‘revise’. I say ‘revise’ because there isn’t too much information to process (yet), but in later lectures it will be beneficial. Also, I’ll use my old textbook Introduction to the Practice of Statistics, Second Edition, whenever it’s helpful to do so. I was going to simultaneously do the Online Video Course ‘Against All Odds: Inside Statistics‘ but it appears that copyright restrictions prevent me viewing this material here in Australia.
More progress…
I am making progress through the High School Level—Basic Math course of lectures. It’s very basic stuff but I still have trouble following some of the problems because I have been conditioned in using different techniques. The lecture I just completed was ‘Exponents and the Order of Operations’, but the stuff that I really want to get to is the Geometry, Algebra and Statistics lectures. I can’t skip straight to them though because I’ll feel better going through the earlier lectures just in case there is something I’ve forgotten and needs to be recalled. It’s pretty time consuming though and I’m not really learning much new (or remembering things that I had forgotten.)
Yay!
I finally completed the lecture series High School Level—Chemistry. I understood everything presented but had a minor problem with the solubility equilibria problems in the last lecture because I couldn’t recall how to rearrange the equations to find an unknown i.e. problems that were essentially mathematical in nature. Other than that, I deepened my understanding of basic chemistry and general problem solving. In high school, and during the first year of my science degree, I rote learned pretty much everything, but these lecturers presented the subject matter in such a way that I began to ‘intrinsically’ appreciate each of the variables such as mass, moles and molarity. This made problem solving far more intuitive. The lecturer, Frank Cardulla, is a brilliant teacher.
