Posts Tagged ‘statistics’
Taught: Using Excel to calculate Mean and Frequency
While on the subject of statistics, here is a resource which can help with teaching a useful facet of spreadsheets — calculating the mean, median, mode, etc. of data.
(Source: mean-and-frequency-in-excel.swf)
This was created using the excellent (and free!) piece of software Wink.
Wink is basically a free version of software like Turbodemo (or for the more Web 2.0 people out there, Jing), which allows you to create ’screencasts’, capturing screenshots and turning them into standalone animations (in Wink’s case, Flash .swf files). These are used in the help files of many pieces of software, like the graphing package Autograph. As well as capturing screenshots, and keypresses, you can add annotations, and link forward/back to different sections of the recording.
Screencasts like this have great potential for demonstrations, not just of technology, but also as ways of recording how to solve maths problems. They also let a teacher run through a problem without having write material on the board constantly. The downside, of course, is that they do require a significant amount of effort to produce, but sites like MathCasts are beginning to offer a number of premade screencasts, which I need to look through at some point!
Tags: Excel, ict, Maths, screencasts, statistics, wink
Taught: Can you generate Binomial data?
Background
This is an way of developing the use of the chi-squared distribution, which can also be used to test whether your students can remember what the Binomial distribution looks like!
Start by challenging everyone in the class to generate some data which they feel could be modelled by a Binomial(5,p) distribution, for some value of p. Calculate the value of chi-squared for the frequencies entered (which involves reviewing how to estimate the mean, and what the formula for Binomial is), and then compare that with the critical value needed for the data to be a ‘good fit’ (to, say, a 5% level).
Interactive Binomial Fitness Calculator
I thought I would set myself the challenge of converting this activity into a form which could be directly placed on a Webpage, like this one. After a few days messing around (and a morning wondering why Wordpress didn’t like my Javascript), I can present the following:
Can you generate data which can be modelled well by a binomial distribution?
Try entering frequencies below for data which can be modelled well by Binomial(5, p), for some p. After entering the numbers, click 'Calculate', and the computer will assess how well your data fits a Binomial by performing a chi-squared test.
| Successes | Frequency |
|---|---|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
(Source: testbinomialmodel.html.)
Note that the condition it is using for goodness of fit is the 5% critical value for chi-squared with four degrees of freedom (6 - 1 because we know the total frequency - 1 because we’re estimating the probability). Note also that it does not combine cells.
Uses
Beyond an initial check of how good students are at modelling a Binomial distribution, this interactive tool can also be used as a tool to explore the Binomial and chi-squared, by systematically altering values and seeing what happens. We can also do something similar, but fix a particular value for the probability of success — this makes it easier to improve by ‘trial and error’ toward a fixed destination, and would also allow us to discuss whether a fit can be too close.
Tags: chisquared, javascript, Lessons Taught, statistics