Calculating Statistics By Hand - Variance and Standard Deviation

In the good old days, statistics had to be calculated by hand - even calculating an average figure may take a long time. Calculating something like variance or a t-statistic could take a lot of time and brain work. Calculators took some of the work out of this, and of course the likes of Excel and SPSS can now to the work in seconds. We (I) still teach statistics in the old way and insist that students learn how to do the various calculations with pen and paper, plus a calculator. My view, and the view of many of my colleagues, is that the ability to understand how statistics work is enhanced by being able to see how each calculation is done, and how the formulas for these calculations are made up.

One of the most important statistics to be able to calculate is Variance. It is used in descriptive statistics, and for me it is vital to be able to calculate it quickly. Learning to do it by hand will lead to greater understanding of how other statistics are calculated. Most importantly of all - hundreds of thousands of students all over the world have to be able to do it in exams without the help of a computer. I have made several videos that show how variance is calculated in Excel (eg, see How To... Display a Range of Descriptive Statistics in Excel 2010), but this is not the way students calculate statistics in an exam.

Aver Document Camera.
Image source: Tiger Direct.

Recording hand written calculations was tougher than I thought it would be. I tried, gave up, and tried again the Aver Classroom Technology Document Camera. There has been one in the College for a few years now, but I've never used it. One of my colleagues, Dr Keith Maycock, has used it for great effect in his YouTube Channel. It is a clumsy gadget to use. Videos are recorded onto a USB and a separate screen was necessary to see what I was doing. The audio was not consistent, and I also found the angle of my hand caused me to block a lot of what I was doing. In the end I created my first video on how to calculate variance by hand. A criticism I have received about my many statistics videos using Excel is that this is not how it is done in an exam. So I have decided to make a new series of videos showing how the various statistics such as variance, z, t, F, r, etc are calculated on pen and paper with just a calculator to help. Here's the first one: