Category Archives: Statistics

General, Maths, Statistics

Current Application of Mind Maps

I've finally completed the second section of the first book, and it's served as a good revision/introduction session. I'm glad I went to the trouble of creating a mind map for the main concepts that were covered. Here's how my mind map grew as I added to it:

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I've used this new mind map to refer back to several times during the exercises I've been set, and even the first assignment question. Admittedly it takes longer to get through all the learning material, as you have to take time out to contribute to the mind map as you go. Though I would say the time spent is worth it.

I also felt that this last image was the maximum size a mind map could take without becoming too cluttered. For the next section of the book, I'll be starting a brand new mind map. I'll try to keep going with this method for as long as I can, but it seems it's very useful.

Statistics

Module Number 7!

Summer is over!

Autumn is here!

That can only mean the new academic year is about to begin! (and the first module of the third and final stage of my degree!)

Up next? Applications of Probability (M343)!

I'm excited about starting this. When I started on this degree, I saw that there weren't many options for stats modules in the final stage unless you were specifically aiming toward a BSc in Statistics. I've read a number of articles discussing how there isn't enough stats in education at the moment and I'm inclined to agree. I'm hoping this will round my skills out nicely.

For all the info on this next module, check out the official page here.

The module website for students is due to open tomorrow, so I'll get access to all my materials and be allocated a tutor. What makes this module a little bit different is that it's a single credit module. The last two modules I've had (mathematical modelling and pure mathematics) were double-credit. So I'm wondering whether the workload will feel really light or not. I'm hoping it will be lighter, so I can contribute on here more frequently than for the last two!

Maths, Statistics

Year Two

After a long break from my first module, I decided to start my next module in February 2014, half-way though the academic year.

My second module was to be Statistics. I was looking forward to this, and wasn't disappointed. The module covered a lot about survey results, and how to conduct surveys effectively and make sense of the data. It also had a biology experiment thrown in there for good measure, the results of which were meant to be used in an assignment.

One of the things that really bothered me though, was their description of statistical variance. To my mind, one measure of variance would be the sum of the difference between the population mean and the sample mean, all divided by the sample count.

In fact, that's not the case. It's not divided by the sample count, it's divided by the sample count minus one. This seemed totally counter-intuitive, and apparently the full explanation was outside of the course material!!! Frustrated I scoured the web looking for an explanation... Eventually I came across a decent youtube vid. Thanks youtube!

To summarise, this video proves that sample variation s^2 is an unbiased estimator of the population variation \sigma^2 as shown below:

    \[<span class="ql-right-eqno"> </span><span class="ql-left-eqno"> </span><img src="http://adrianbell.me/wp-content/ql-cache/quicklatex.com-8309d8e21d5c74b4a21588f648103d5a_l3.png" height="45" width="261" class="ql-img-displayed-equation quicklatex-auto-format" alt="\begin{align*} E(s^2) =& E \left( \frac{ \sum_{i=1}^n( x_i - \bar{x} )^2 }{n-1}\right) = \sigma^2 \end{align*}" title="Rendered by QuickLaTeX.com"/>\]

See that pesky "n-1" divisor? Check out the full explanation here.

So after my study starting in February and ending in September, I felt I'd had a decent introduction to statistics.

Although, something that does surprise me is that looking ahead at my possible future module choices... statistics doesn't really crop up again for the rest of my maths degree. With the growing importance of statistics in modern society (let alone mathematics itself!) I would have expected a lot more of those modules on offer. Having said that, there is a separate BSc (hons) Mathematics and Statistics that the OU offers, but this appears to almost be purely statistics and doesn't give much variety. -certainly wouldn't be good for me.

In fact, there are  only two real interesting modules on this Maths and Stats degree course, one of which is the final year module "Mathematical Statistics" (M347) that introduces Markov Chain Monte Carlo, which is an area of interest. I suppose after my ten-year degree, if I'm still desperate for more, I can sign up for it as a stand-alone module. 🙂