MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Simplifying rational expressions combines everything learned about factoring common factors and polynomials. When simplifying rational functions, factor the numerator and denominator into terms multiplying each other and look for equivalents of one (something divided by itself). Include parenthesis around any expression with a "+" or "-" and if all terms cancel in the numerator, there is still a one there.
When you're asked to describe a data set there's a couple of different ways you can describe the middle. What we call "measures of center," those options are mean, median and mode and a lot of times when you guys see advertisements they chose a tricky one to publish trying to sway their audiences. Statistics is all about manipulating data to show what you want to show. For example let's say we were to look at the salaries of the LA Galaxy soccer team some of you guys know that Beckham makes millions and millions of dollars. But some of the other guys who are on the same team barely makes 17,000 maybe 19,000 they make like a tenth of what Beckham makes. So what happens is that is you were to advertise the average salary of the LA Galaxy the really high value for Beckham which we call an outlier would mess up the average. It would actually pull the average larger. Whereas in reality the average salary for the LA Galaxy isn't very big. It just gets pulled up because when we add them all together Beckham's high number pulls up the other values.
That's why it would be more accurate to describe that center of salaries using what we call a "median." A median is effective if you have a high outlier or a low outlier. Median doesn't get affected by that, let me show you how it's done. The median is the middle value when a list of numbers is arranged from smallest to largest. If there are an even number of values in the list the median is the average of the middle two values. That'll make a lot more sense once you start looking at example problems but one way you could remember that median is the middle is by thinking about road medians. If you guys are drivers yet you probably know what I'm talking about with the road median right.
If you have a road like this and traffic goes like that way and that way sometimes they have this little median in the middle with flowers and trees and birds. That's the median it's in the middle just like when you make a list of values the median is the middle value. So keep that in mind when you're doing problems also keep that in mind if you're go into advertising you might chose to advertise the average salary instead of the median salary if you have an outlier data that kind of warps your data set.
